(1) Individual action by residential postal users for the purposes of participating in postal matters and communicating their views is rendered impracticable by reason of the disproportionate expense of taking such action.
(2) Such participation and representation can be best secured by the creation of a permanent, not-for-profit organization which is under the democratic control of its membership, solely responsive to that membership's goals, and which is funded by voluntary contributions.
(3) The formation of such an entity by consumers acting voluntarily is impeded because consumers have neither the resources nor an efficient mechanism to contact all residential postal users, raise initial funds and join such an entity.
(4) In order to create such an entity, it is necessary to establish a democratically structured organization and to provide for the dissemination, to all postal users, of information as to the formation and purposes of such organization and to provide an efficient means for joining and contributing to such organization.
(1) To assist in establishing adequate and affordable postal service to all residential postal users.
(2) To foster and encourage active citizen participation in postal matters and to facilitate effective representation and advocacy of the interests of residential postal users before regulatory agencies, Congress, the courts and other bodies; and for these purposes create a permanent not-for-profit organization.
(3) To create an efficient funding mechanism for the organization, involving no compulsory burden whatsoever [*296] on the taxpayers of the United States, whereby individual residential postal users and others may voluntarily contribute to the organization.
(4) To ensure that public policies affecting the provision, quality and cost of postal services fairly reflect the needs and concerns of those users.
complaints; and to provide for residential postal users' membership in such Corporation and residential postal users' direction of the actions of such Corporation.
(a) "Individual residential postal user" means any person who sends or receives letters, packages and other items through the United States Postal Service for non-business purposes.
(b) "Private mail delivery service" means any establishment which regularly delivers second-class, third-class, fourth-class, overnight or other category of mail for profit.
(c) "Agency" means any local, state or federal department, commission, office, authority or other public body with the legal authority to establish or alter rates or services for the provision of postal services within the United States.
(1) The establishment or alteration of rates and charges for the provision of postal services within the United States.
(3) Adjudication of complaints, claims, disputes and petitions of residential postal users.
(4) The gathering of information on matters that affect the interests of individual residential postal consumers.
[*297] (e) "The Corporation" means the Postal Office Consumer Action Group, Inc.
(f) "Member" means any person who meets the requirements for membership in the Corporation set forth in this Act.
(g) "Director" means any member of the Corporation duly elected or appointed to the board of directors of the Corporation.
(h) "Delegate" means any person duly elected or appointed as a delegate under the provisions this Act.
(i) A "District" means a district designated by the board of directors pursuant to this Act.
purpose of electing a candidate as a director or delegate, or a contract, promise, or agreement therefore.
made for the purpose of electing a candidate as a director or delegate.
(l) "Political committee" means any committee, club, association, or other group of persons which makes campaign expenditures or receives campaign contributions during the year before an election of directors or delegates.
(a) There is hereby created a not-for-profit membership corporation to be known as the Post Office Consumer Action Group Inc., herein referred to as the Corporation.
(b) The membership of the Corporation shall consist of all individuals of sixteen years of age or older who have contributed to the Corporation at least an annual membership fee at such times as shall be set by the board of directors, provided, that any person may resign from membership.
(1) Represent and promote the interests of individual residential postal users. All actions by the Corporation under this Act shall be directed toward such duty.
(2) Inform, insofar as possible, all residential postal users [*298] about the Corporation, including the procedure for obtaining membership in the Corporation.
(3) Establish an annual membership fee which shall be set at a level that provides sufficient funding for the Corporation to effectively perform its powers and duties, and is affordable for as many residential postal users as is possible, but nevertheless not less than eight dollars.
(4) Have all rights and powers accorded generally to, and be subject to all duties imposed generally upon, not-for-profit membership corporations under the laws of the United States.
governor, employee or agent of the Postal Service.
users, and public information activities concerning the interests of individual residential postal users.
(4) To contract for services which cannot reasonably be performed by its employees.
(5) To represent the interests of individual residential postal users before the United States Postal Service, Postal Rate Commission, Congress, state legislatures, federal and state courts, and other agencies, except as this Act otherwise provides.
(6) To support or oppose ballot propositions concerning matters which it determines may affect the interests of individual residential postal users.
(7) To transmit complaints by individual postal users concerning the United States Postal Service and private postal delivery services to the United States Postal Service and other appropriate agencies. Any such agency shall promptly inform the Corporation of its response to such complaints.
(8) To initiate, to intervene as a party, to maintain, or to [*299] otherwise participate on behalf of residential postal users in any proceeding which affects the interests of residential postal users.
(b) The Corporation shall have, in addition to the rights and powers enumerated in this Act, such other incidental powers as are reasonably necessary for the effective representation of the interests of individual residential postal users.
(c) The Corporation shall not sponsor, endorse, or otherwise support, nor shall it oppose, any political party or candidacy of any person for public office.
participate. The agency shall notify or cause notice to be given to the Corporation at least thirty days before the scheduled date of such proceeding or within five days after the date and calendar for such proceeding is fixed, whichever is later. In addition, the agency shall give notice or cause notice to be given within five days to the Corporation of any filed statement proposing to modify or increase rates, services, schedule of rates or any other rating rule or to adopt or amend any rate or service rule or regulations.
(1) The Corporation may intervene as of right as a party or otherwise participate in any proceeding of the United States Postal Service, Postal Rate Commission or agency which the Corporation reasonably determines would affect the interests of individual residential postal consumers.
(2) The intervention or participation of the Corporation in any such proceeding will not affect the obligation of the United States Postal Service, Postal Rate Commission, or other agency to operate in the public interest.
Corporation shall have the same rights regarding representation by counsel, participation in pre-hearing confernd cross-examination of witnesses, oral and written arguments, participation in settlement negotiations, and other aspects of the proceeding as are accorded to other interveners under the laws of the United States or, in instances where a proceeding is held by state or local public body, under the laws of that state, except as otherwise provided in this Act.
The Corporation shall be deemed to have an interest sufficient to maintain, intervene as of right in, or otherwise participate in any civil action, proceeding or appeal for the review or enforcement of any decision by the United States Postal Service, Postal Rate Commission, or other public body which the Corporation determines would substantially affect the interests of individual residential postal users.
(a) If the Board or Executive Director reasonably determine that bringing a civil action against the United States Postal Service on behalf of any member or group would further the general purposes of this Act, the Corporation shall provide the legal services necessary and the expert witness services reasonably appropriate for prosecution of the action.
(b) Any member who receives money due to a settlement or judgment attained with assistance in litigation provided by the Corporation as described in subsection (a) of this Section shall reimburse the Corporation for its expense in prosecution of the action, provided, that such reimbursement shall not exceed ten percent of the money received by the member.
(a) The Corporation shall have the authority to prepare a statement concerning the organization and activities of the Corporation, including the purpose, history, nature, [*301] structure and achievements of the Corporation, and other matters which may affect the interests of individual residential postal users. The statement shall indicate that the statement is not connected to the Postal Service or any governmental agency. The statement shall indicate the procedure for becoming a member of the Corporation. The statement shall not contain an individual postal address.
(b) of this section. The Commission shall be deemed to have approved the statement unless it disapproves the statement within fourteen days of receipt.
(c) The Postal Service shall, subject to subsection (d) of this section, deliver to each individual post office or postal facility in the United States, a quantity of the mailings, pursuant to subsections (a) and (b) of this section, which approximately equals the number of residential addressees in the region served by the postal facility. Individual post offices and postal facilities shall deliver such mailings to every residential address in their district during regular delivery rounds.
(d) The United States Postal Service may implement a procedure for distributing such mailings o(c) of this section, unless such other procedure would be more costly to the Corporation or would be a slower or otherwise less efficient means of distributing such mailings.
(e) The United States Postal Service shall be required to distribute such mailings within 60 to 90 days of the date on which the statement is given to the Postal Service by the Corporation.
(f) The United States Postal Services shall not be required to deliver such mailings pursuant to subsections (c) and (d) of this section at intervals of less than six months This provision shall not affect the obligation of the United States [*302] Postal Service to deliver any mailings for the Corporation for which the Corporation pays postage fees.
(g) The United States Postal Service shall bear all cost incurred in distributing mailings pursuant to subsections (c) and (d) of this Section.
(h) Any disputes arising from the operations of subsections (a) through (g) of this section shall be resolved by negotiations between the Corporation and the United States Postal Service if possible, or by a civil proceeding in the courts of the United States. Neither the United States Postal Service nor the Corporation may fail to comply with the provisions of this Act by reason of such a dispute.
(i) An individual may contribute to the Corporation by sending a payment to any office of the Corporation. He or she may list the names of additional contributors in his or her household who are sixteen years of age and older and the amount each has contributed.
(a) No official or employee of the United States Postal Service, or any other public official or employee or officer, or any employee or agent of any private mail delivery service may interfere or threaten to interfere with or cause any interference with mail delivery to, or penalize or threaten to penalize or cause to be penalized, any person who contributes to the Corporation or participates in any of its activities, in retribution for such contribution or participation.
(b) No official or employee of the United States Postal Services, or any other public official or employee or officer, or employee or agent of any private postal delivery service may prevent, interfere with, or hinder the activities described in this Act.
(1) A person who violates subsection (b) or (c) of this Section shall be subject to a civil penalty of not more than $ 10,000. Each such violation shall constitute a separate and continuing violation of the Act.
(a) The affairs of the Corporation shall be managed by a board of directors. There shall be twenty directors.
(b) The term of office of elected directors shall be three years and no member shall serve more than two consecutive terms. One third of the directors first elected to the board shall serve a one-year term; one third of such directors shall serve a two-year term; and one third of such directors shall serve a full three-year term. The directors shall draw lots upon their installation in office to determine the length of their first terms. The term of office of directors appointed pursuant to this Act shall end when the first elected directors are installed in office.
(c) Directors shall meet the qualifications for delegates set forth in this Act.
(d) The directors shall serve without salary, but each director may be entitled to reimbursement for actual and necessary expenses. The board of directors shall establish standard allowances for mileage, room and meals and the purposes for which such allowances may be made and shall determine the reasonableness and necessity for such reimbursements.
(e) No director nor members of his or her immediate family shall, either directly or indirectly, be employed for compensation as a staff member or consultant of the Corporation.
(f) Any director who shall handle, disburse, or receive money on behalf of the Corporation shall be bonded. Such bond shall be a cost to the Corporation.
(g) Each director shall represent the interests of residential postal users of the United States.
(h) Each director shall have one vote of the board of directors.
(i) Elected directors shall be installed in office by the president of the outgoing board of directors.
(a) To establish the policies of the Corporation regarding appearances before the Postal Rate Commission, other agencies, the courts, and other public bodies, and regarding the activities which the Corporation has the authority to perform under this Act.
(c) To keep minutes, books, and records which shall reflect all the acts and transactions of the board of directors which shall be open to examination by any member during regular business hours.
(d) To make all reports, studies, data pertaining to the finances of the Corporation, and other information compiled by the Corporation, available for public inspection during regular business hours.
(e) To maintain for inspection by membership quarterly statements of the financial and substantive operations of the Corporation.
(g) To prepare, as soon as practicable after the close of the Corporation's fiscal year, an annual report of the Corporation's financial and substantive operations to be made available for public inspection.
(h) To report to the delegates at the annual meeting of delegates on the past and projected activities and policies of the Corporation.
(i) To employ an executive director and to direct and supervise his or her activities.
(j) To hold regular meetings at least once every three months on such dates and at such places as it may determine. Special meetings may be called by the president or by at least one-quarter of the directors upon at least five days' notice. One-half of the directors plus one shall constitute a quorum. All meetings of the board of directors and of its committees and subcommittees shall be open to the public. Complete minutes of the meetings shall be kept.
(k) To carry out all other duties and responsibilities imposed upon the Corporation and the board of directors by this Act.
required [*305] by this Act within three years of the appointment of the complete interim board of directors, the Corporation shall be dissolved after having satisfied its debts, liabilities and obligations to the extent possible from funds made available to the Corporation. Individuals considered for appointment for the board of directors shall have the same qualifications as candidates for the permanent board of directors pursuant to this Act, and shall, to the extent possible, represent each region of the United States.
(1) Inform the residential postal users of the United States of the of the existence, nature, and purpose of the Corporation, and encourage residential postal users to join the Corporation's activities and to contribute to the Corporation.
(2) As soon as possible after appointment, organize for the transaction of business.
(5) Make all necessary preparations for the first election of delegates and directors, oversee the election campaign and tally the votes.
(7) Carry out all other duties and exercise all other powers accorded to the board of directors of this Act.
(a) The Corporation shall elect one delegate from each congressional district in the United States, including the District of Columbia.
(b) The delegates shall serve without salary.
(c) The term of office of delegates shall be two years and no delegate shall serve more than two consecutive terms.
(d) No delegate nor members of his or her immediate family shall, either directly or indirectly, be employed for compensation as a staff member or consultant of the Corporation.
(e) Any delegate who shall handle, disburse, or receive money on behalf of the Corporation shall be bonded. Such bond shall be a cost to the Corporation.
(a) To publicize the activities of the Corporation in their districts.
[*306] (b) To encourage members in their districts to participate in the Corporation's programs and activities.
(c) To act as a liaison between the board of directors and members in their districts. To transmit to the board of directors comments, writings and suggestions concerning the Corporation from members in their districts and to inform such members of the board's response to their statements.
(d) To vote at the annual meeting of delegates and at special meetings of delegates called by the board on matters involving basic changes in the policies and operations of the Corporation. A majority vote of the delegates shall be necessary to institute such changes.
(e) To vote on other items submitted to delegates by the board of directors at annual and special meetings. A majority vote of the delegates shall indicate approval by the delegates of such items.
(f) To carry out all other duties and exercise all other powers accorded to delegates under this Act.
shall set a date for the first election of delegates and shall notify every member. The date set for the election shall be not less than four months nor more than six months after such notification.
(b) Each general election of delegates other than the first election shall be held not less than eleven months and not more than fourteen months after the last preceding general election. The date of such elections shall be fixed at least four months in advance of the date chosen for the election.
(c) Within eleven months of the first elof twenty members. Only delegates shall be eligible to run for the board of directors. Any delegate may nominate himself or herself or any other delegate for election to the board.
(d) Subsequent elections of directors shall be held at not less than eleven months and not more than thirteen months after the last preceding general election. Elections may be held at the annual meeting of delegates if the elections would conform to the requirement of this subsection.
(a) No present employee, director, consultant, attorney, accountant, real estate agent, shareholder, bondholder of the Postal Service or Postal Rate Commission shall be eligible to be a delegate or director. No delegate or director nor any candidate for delegate or director may hold an elective public office or be a candidate for an elective public office or be appointed to hold a public office.
(1) Meet the qualifications for candidates.
(2) Submit a petition for nomination.
(3) Be a member of the corporation and resident of the United States district which he or she seeks to represent as a delegate.
(4) Submit a statement of financial interest and a statement of personal background and position.
(5) Affirm, under penalty of perjury, that the information contained in the statement of financial interest and personal background and position is true and complete.
(2) Be a member of the corporation and a delegate.
(3) Submit a petition for nomination.
(4) Submit a statement of financial interest and personal background and position.
(a) The interim board of directors and every subsequent board of directors shall make available for inspection by any member, upon request, a list of the current members in that member's district.
(b) A candidate for election as a delegate shall submit to the board, no later than sixty days prior to the election, a petition for nomination signed by at least [five percent] of the members residing in his or her district. Upon receipt of a member's nominating petition, the board of directors shall certify that such member is a nominated candidate for delegate.
(c) A candidate for election as a director shall submit to the [*308] board, no later than sixty days prior to the election, a petition for nomination signed by at least [five percent] of the delegates. Upon receipt of a member's nominating petition, the board of directors shall certify that such member is a nominated candidate for delegate.
(a) The occupation, employer, and position at place of employment of the candidate and of his or her immediate family members.
(c) An affirmation, subject to penalty of perjury, that the information contained in the statement of financial interests is true and complete.
(d) Such other information as the board of directors shall require candidates to disclose, which disclosure is required of other public officials at the time, and shall be in the judgement of the board of directors in the best interests of the Corporation.
A candidate for election as delegate or direcection, on a form to be provided by the board of directors, a statement concerning his or her personal background and positions relating to postal issues or the operations of the Corporation. The statement shall contain an affirmation, subject to penalty of perjury, that the information contained in the statement of personal background is true and complete and that the candidate meets the qualifications prescribed for delegates and directors.
Sec. 21. Restrictions on and Reporting of Campaign Contributions and Expenditures.
(a) No candidate for delegate or director may accept more than [$ 100.00] in campaign contributions from any person or political committee during the year preceding the date of the election.
[*309] (b) Each candidate for election to the board of directors or as a delegate shall keep complete records of all contributions to his or her campaign of fifty dollars or more during the year preceding the election. Such records shall be available for inspection by the public.
(c) Each candidate shall keep complete records of his or her campaign expenditures, and such records shall be available for inspection by the public.
(d) Each candidate, no earlier than the next day succeeding the election and no later than thirty days after the election, shall submit to the board of directors, on a form provided by the board of directors, an accurate statement of his or her campaign contributions accepted and campaign expenses incurred, and shall affirm to the board, subject to penalty of perjury, that he or she has fully complied with the requirements of this subsection.
(e) No candidate shall accept campaign contributions from the Postal Service, the Postal Rate Commission, or a private postal delivery service.
(f) If the board of directors determines that the candidate's campaign expenses have exceeded the limits contained in this section, the candidate shall be disqualified and may be required to pay the expenses incurpersonal background and position. The Corporation may pursue all civil remedies to recover the cost of mailing the candidate's statement of personal background and position. In the event of disqualification, the board of directors shall call a special election to be held not fewer than four months and not more than six months after the determination of disqualification.
(g) No candidate may use any campaign contribution for any purpose except for campaign expenditures.
(1) An official ballot listing all candidates for delegate from the member's district who have complied with the requirements of this Act.
(2) Each such candidate's statement of financial interests.
(b) Each residential postal user who is a member of the Corporation on the thirtieth day preceding a special or general election may cast a vote in such election by returning his or her official ballot, properly marked, to the principal office of the Corporation by eight p.m. of the date fixed for the election. Voting shall be by secret ballot. The candidate receiving the greatest number of votes in each district shall be declared elected as a delegate.
(c) The board of directors may prescribe rules for the conduct of elections and election campaigns not inconsistent with this Act.
(1) An official ballot listing all candidates for director who have complied with the requirements of this Act.
(b) Each member of the Corporation who is a delegate on the thirtieth day preceding a special or general election may cast a vote in such election by returning his or her official ballot, properly marked, to the principal office of the Corporation by eight p.m. of the date fixed for the election, or by casting such vote in person if an election is held at an annual or special meeting of delegates. Voting shall be by secret ballot.
(c) Each delegate may vote for a maximum of twenty candidates for director and may cast only one vote for each candidate. If over twenty candidates each receive at least thirty percent of the vote on the first ballot, the twenty candidates with the highest number of votes shall be elected to the board. If less than twenty candidates receive at least thirty percent of the vote on the first ballot, the second ballot shall be conducted to elect candidates to the remaining positions on the board. If there are fifteen or more remaining positions left after the first ballot, then the names of the forty [*311] candidates, excluding those already elected, who received the highest number of votes in the first ballot shall be placed on the second ballot, and the candidates receiving the highest number of votes on the second ballot shall be elected to the remaining positions. If there are less than forty candidates for the remaining positions, the names of all remaining candidates shall be placed on the second ballot. If there are less than fifteen remaining positions left after the first ballot, then the names of the twenty-five candidates, excluding those already elected, who received the highest number of votes on the first ballot shall be placed on the second ballot, and the candidates receiving the highest number of votes on the second ballot shall be elected to the remaining positions. If there are less than twenty-five candidates for the remaining positions, the names of all remaining candidates shall be placed on the second ballot.
(d) The board of directors may prescribe rules for the conduct of elections and election campaigns not inconsistent with this Act.
The president of the board of directors shall install in office within thirty days after the election all elected candidates who meet the qualifications prescribed in this Act.
Upon receipt by the president of the board of directors of a petition to recall any director with the valid signatures of at least forty percent of the delegates, forty percent of the members of the district from which such director was elected as delegate, or ten percent of the Corporation's total membership, the president shall call a special election, to be held not less than four months and not more than six months after receipt of the petitior to serve out the term of the recalled director; provided, that no petition to recall a director may be filed within six months of his or her election. A director may become a candidate in an election following his or her own recall. A director recalled shall continue to serve until the installation in office of his or her replacement. A director who has been recalled shall be allowed to complete his or her term of office as a delegate, unless the petition for recall clearly states that its purpose is to recall a person from the office of delegate as well as director. No delegate removed from office shall be allowed to continue serving as director.
directors present and voting. The successor shall be installed in office by the president of the board of directors.
Upon receipt by the president of the board of directors of a petition to recall any delegate with the valid signatures of at least forty percent of the members from such delegate's district, the president shall call a special election for the district to be held not less than four months and not more than six months after receipt of the petition, for the purpose of electing a delegate to serve out the term of the recalled delegate; provided, that no petition to recall a delegate may be filed within six months of his or her election. A delegate may become a candidate in an election following his or her own recall. The Delegate recalled shall cllment in office of his or her successor.
Sec. 28 Vacancies of Delegates.
When a delegate dies, resigns, is disqualified, or otherwise vacates his or her office, the board of directors shall hold, within three months of the date on which such vacancy was created, an election in the delegate's district for the purpose of electing a successor for the remainder of the delegate's term of office. The successor shall be installed by the president of the board of directors.
(a) An annual meeting of delegates shall be held on a date and at a place within the United States of America to be determined by the board of directors.
(b) All delegates shall be eligible to attend, participate in, and vote in the annual meeting of delegates. Two-thirds of the delegates shall constitute a quorum. Each delegate shall have one vote at such meeting.
(1) By request of any director or delegate not less than five days and not more than four months in advance of the date of such meeting.
[*313] (2) By petition containing the valid signatures of at least twenty percent of the members of any district or at least one percent of the total membership. Such petition must be filed with the board of directors not less than two days and not more than five months in advance of the date of such meeting.
(d) The form of the annual meeting of delegates shall be provided in the laws of the United States regarding not-for-profit membership corporations.
(e) The annual meeting of delegates shall be open to the public. Members shall be given a reasonable opportunity at such meeting to present their comments, criticisms and suggestions concerning the Corporation, but members may not vote at such meeting.
(f) The treasurer shall reimburse delegates for actual expenses necessarily incld a special meeting of delegates to consult with delegates on matters concerning the Corporation's policies, activities, and operations. The board of directors shall set a time and place for a special meeting and shall inform every delegate of such time and place not less than fourteen days and not more than sixty days in advance of the date of such meeting. The directors shall be required to call a special meeting when they receive a petition containing the valid signatures of over fifty percent of the delegates or at least five percent of the members or when the majority of delegates vote for such a meeting. The meeting shall be held not more than thirty days after the filing of such petition or the date of such vote.
(a) At the first regular meeting of the board of directors at which a quorum is present and subsequent to the initial appointment of directors, and at the first regular meeting of the board of directors at which a quorum is present subsequent to the installation of new directors following each annual election, the board shall elect by a majority vote of members present and voting from among the directors a president, a vice-president, a secretary, and a treasurer. The board also has the power to elect a comptroller and such other officers as it deems necessary.
(b) Officers shall be installed by the president immediately upon their election. The term of office for officers shall be one year; provided that an officer may resign, or may be [*314] removed from office by a two-thirds vote of all the directors. After an officer's term of office has expired, the officer shall continue to serve until his or her successor is installed.
(c) When an officer dies, resigns, is removed, or otherwise vacates his or her office, the board of directors shall elect a successor to serve out such officer's term of office.
(d) The officers shall exercise such powers and perform such duties as are prescribed by this Act or are delegates to them by the board of directors.
(a) The executive director hired by the board of directors shall have the same qualifications as a candidate. The executive director may not be a candidate for the board of directors or delegate while serving as executive director. The by-laws of the Corporation shall provide a method for discharging the executive director, but in no event shall such discharge occur unless one-half of the directors plus one shall have consented to such discharge.
(b) The board of directors shall require all applicants for the position of executive director of the Corporation to file a financial statement. The board of directors shall require the executive director to file a financial statement annually.
(1) To implement the policies of the board of directors.
(2) To employ and discharge employees of the Corporation.
(3) To supervise the offices, facilities and work of the employees of the Corporation.
(4) To have custody of and maintain the books, records and membership rolls of the Corporation.
(5) To prepare and submit to the board of directors annual and quarterly statements of the financial estimates for the operations of the Corporation.
(6) To attend and participate in meetings of the board of directors as a non-voting director.
(7) To exercise such other powers and perform such other duties as the board of directors delegate.
(a) The not-for-profit corporation law applies to the Corporation; provided, that if any provision of the not-for-profit corporation law conflicts with any provision of this Act, the conflicting provision of the not-for-profit law shall not apply [*315] in such case. If any provision of this Act relates to a matter embraced in the not-for-profit corporation law but is not in conflict therewith, both provisions shall apply.
(b) Nothing in this Act shall be construed to limit the right of any individual or group or class of individuals to initiate, intervene in, or otherwise participate in any proceeding before any regulatory agency or court; nor to require any petition or notification to the Corporation as a condition precedent to such right, nor to relieve any postal agency, court or other public body of any obligation, or affect its discretion to permit intervention or participation by a postal user or class of postal users in any proceeding or activity, nor to limit the right of any individual or individuals to obtain administrative or judicial review.
(c) The intervention or participation of the Corporation in a proceeding or activity shall not affect the obligation of any regulatory agency or other public body to operate in the public interest.
Sec. 33. Corrupt Practices and Conflor agent of the Corporation if the offer or gift influences, or is intended to influence, the action or judgement of the director, employee or agent of the Corporation in his or her capacity as director, delegate, employee or agent of the Corporation.
(b) No director, delegate, employee or agent of the Corporation may solicit or accept anything of monetary value form any person if their solicitation or acceptance influences, or is intended to influence, the official action or judgement of the director, employee or agent in his or her capacity as director, employee or agent of the Corporation.
(c) Any person who knowingly and willfully violates this section shall be subject to a civil penalty of not more than $ 10,000.
(d) The board of directors shall remove from any director, delegate, employee or agent of the Corporation violating the provisions of this section.
A violation of any provision of this Act pertaining to conduct by the Postal Service of officers or employees thereof shall be subject to a civil penalty of nor more than $ 10,000 for each violation.
This Act, being necessary for the welfare of the United States and its inhabitants, shall be liberally construed to effect its purposes.
If any clause, sentence, paragraph or part of this Act or the application thereof be adjudged by a court of competent jurisdiction to be invalid, such judgement shall not affect, impair or invalidate the remainder, and the application thereof, but shall be confined in its operation to the clause, sentence, paragraph or part thereof directly involved in the controversy in which such judgement shall have been rendered.
This Act shall become effective on the date of its enactment.


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Maria: The wine holder. My husband Terry created it for me and it holds all our wine glasses and wine bottles. It is a refurbished horse trough that came from an old liquor company and it was made into a shelf. I love collecting and I found myself with a vast number of wine glasses but they were being stored in cabinets and not seen or used. I think it is a very special piece because he made it himself and it's a great conversational piece. How many can say they have a horse trough inside their house?
Maria: Love books. There is something about looking at an interesting cover and turning each page. I unfortunately, do not get to read as much as I want but right now I'm reading Sage Living by Anne Sage, an interior design book that describes the connection between happiness and the home. I love the fact that we can create spaces in our home that we love.
Maria: We listen to Terry's old vinyl records. We will find ourselves on a Saturday night turning on his stereo (yes, one with three foot tall speakers) and listen to some classic music from the Rolling Stones, Pretenders, Van Halen, Led Zeppelin and many other great artists. We truly enjoy something so simple where time stands still for a short while in this crazy place called Life. I do own one album from the 80's, Air Supply's Lost in Love but I'm not allowed to play it on his turntable. What! Loved their love songs.
Maria: Don Pedro has great fresh food. The Jade Burrito is delicious and the Margaritas are wonderful!
Maria: People unite when someone is in need. We recently went to a benefit where they had a wonderful turnout for someone locally. There's an ex-musician who is ill (and has subsequently passed away) and local musicians who had bands in the 80's and 90's in Effingham gathered again after many years and played once again to support him. The music was great and the positive energy was awesome! We saw that family, friends, and the community came to support and raise money for a good cause.
Wild card question... What do you want people to know about you?
Maria: I truly enjoy entertaining. Nothing is better than a house full of people that you love. Whether be the holidays, birthday parties or simple get togethers they are always done with thought and care. Having people in your home that care about you means the world to me. We have been known to throw milestone birthday, anniversary, and even New Year's Day parties. The more people the merrier!
Oh, but she tried to get him to write a response to my questions. She's actually the first wife who's included her husband at all. Luckily for us Maria Bushur did manage to get her husband, Terry, to talk to me about their home. His family's third generation, 1920s milk barn that he spent weekends and evenings for two years and then brought in help for the fourth and fifth year of renovation to convert. Whew.
Terry poured and scored the concrete flooring. The posts are original to the barn, however where it met the ground had slightly rotted away so Terry created these wooden encasements for them. The church pew was twice as long so Terry cut it down. On the far left wall is a picture from their wedding, which took place in the home.
The family farm is located on the north side of town where Effingham turns from shopping/subdivisions into farmland. Maria wanted to restore the old farmhouse on the property and make it pretty, but due to major structural problems, that was not in the cards. So Terry invited the Sigel Fire Department to come tear down the farmhouse as practice and he set his sights on the barn. Maria, through blind faith, followed him along.
Now imagine, this was back in 2006, when few people around here, if any, were turning barns into homes or building "shouses" (shed/house). The barn's last function was as a barn so there were still mangers, stalls and hay inside. I can kind of see Maria's difficulty in wrapping her mind around this huge project.
Up top is the "before" picture of the former milk barn and bottom is amid renovation in 2007.
And the beautiful "after". Note the two balconies and the silo. Hanging from the roof of each balcony is an original piece from the barn's hay carrier system - a reminder of the work-horse this house used to be.
Let me tell you a little about this couple. In my mind Maria is a Peruvian version of Eva Gabor from Green Acres. She's always impeccably dressed and done up, she tells you what she thinks yet she's very nice about it and she lives on an old farm. Terry is a full time journeyman and concrete finisher, lover of vinyl records and a man of very few words. This marriage is the perfect example of opposites attract.
Maria: Bold orange, bling, frames and family photos. Terry: Beautifully reimagined natural materials. See the wine holder trough in the top photo? Terry crafted it out of an old trough.
The painted bamboo china cabinet is one of Maria's many fabulous found objects and she's filled its glass shelves with choice vintage serveware pieces in orange, chrome (see those cocktail shakers in the back?), amber glass (cake platter), clear glass and the most beautiful collection of cake stands. Check out how it all pops thanks to the cabinet's light.
Terry was definitely the one with the vision for the place. Maria walked into the not-yet-finished house one day to find someone installing the railing on their staircase. When she learned that it was hog fencing she about lost it. There was no way she was going to live in a house with hog fencing. But it stayed and she's grown to love the slightly industrial feel it lends to the home.
Lots of natural elements here with Maria's pops of color. Terry made the bench and Maria found the unique triangular drop-leaf table next to it.
Terry's barn-converting methods involved repurposing/restoring a lot of different materials. Like taking off the existing tin roof and flipping it over and pressure washing all of the barn wood four to five times (FOUR TO FIVE TIMES!) and then sealing it. He used nontraditional materials (um, hog fencing) and reused things as often as possible. The sides and front of the bar are made from the door of the old farmhouse. Being a self-employed journeyman and long term concrete finisher, he made the floors. Yes, he made concrete look like brick and he installed underfloor heating. He also poured the concrete countertops. This was a man before his time.
Nope, not brick. Concrete. A bubble appeared in the floor so they turned it into a feature by adding the penny.
Here are the old farmhouse doors reimagined. And check out the concrete counter.
Maria confesses that his friends probably thought what he was doing was crazy, but they, plumbers, carpenters, electricians and dry wallers all came together with the knowledge and expertise of general contractor, Ron Goldstein, and completed the project. In the end Maria's only regret is that they didn't install a more barn-like door and his is that he should have only built one balcony instead of two. Because in his words, "you can only use one at a time". Men.
Their fabulous front door area decorated for fall.
Although her home is a former barn, Maria didn't want it to be too country looking. Hence the absolutely fantastic, sleek kitchen cabinets from Lustig Custom Cabinets in Effingham. They are contemporary slab door style Maple cabinets with a dark stain and a metallic fleck in the finish. Nothing visible to the eye but it uniquely catches the light. Who knew there was such a thing? The hardware is Key West.
Here are the gorgeous cabinets. And above the brand new cabinets sit serveware from the 1950s and 1960s. On the counter are vintage candy containers (one she found at Fresh Digs) that contain important kitchen items like dishwasher pods. The large still life on the counter is her most recent vintage find.
Upon closer inspection of this home's accessories you find many of Maria's mid-century vintage finds mixed in with rustic pieces from the farm interspersed around the contemporary furniture. She's managed to tie all of these otherwise disparate elements together thanks to the unifying barn wood and one predominant color – orange. She loves orange. And she loves hunting down vintage treasures and great deals. Many of her vintage pieces were found at auctions and garage sales. Ask her about her near death online garage sale experience. Plus she's got many collections of very cool things from Peru.
Maria loves family photos and frames. Above the mid century dresser hangs an aerial photo of the farm and to the left is a collection of vintage swung glass vases. The round mirror with the floral detail came from Peru.
Here she is standing in front of the vintage pull-down map she got at Fresh Digs. Old farm implements found on the property hang from the ceiling. The home has yet another floor presently serving as storage and access to the balconies.
Great colors going on in this bathroom. The paint color is "Cardboard" by Sherwin Williams. The red cross window came from Fresh Digs and the old books on the little round table came from an auction.
As Maria puts it, "our house has a story" and Terry and Maria are both very proud to be living in something they created. And if Terry ever pulls the trigger on his dream of building a walkway to a hot tub built on top of the silo, then this may just become the coolest barn/house ever built.


...a complete guide to myspace layouts, stock photography, clipart, free pictures, scans, and web graphics.
Layout Description: An american layout through and through. Red borders surround the boxes in this layout with a transparent white background so you can represent who your voting for in the 2008 election. There is a white background with a large image of an american flag behind Hillary Rodham Clinton.
This is the name you chose when you signed up for your MySpace account. The one Tom said you can never change.
This is the number at the end of the URL in your address bar on your page or your friends page.


There is much positive news these days about regenerative agriculture. Ranchers and farmers are finding new ways to restore carbon to the earth and work with ecosystems rather than plow and destroy them.
Learn how holistic rangeland management creates healthier grasslands and helps reverse climate change by building soils and drought resilience at a special event in support of mission and programming of Pacific Horticulture Society.
On Saturday May 11 Gabilan Ranch in San Juan Bautista will give an all day tour of their sustainable cattle ranch to members of PHS that will include lunch and refreshments at the end of the day.
More info and register online at pachort.org /gabilan2019 or call 510-849-1627.
The event is $250 for members, $300 for non members. Non members can become a member for $40 with the discount code "IwantPHS" when joining.


text:
\section{Introduction}

Neutrinoless double-beta decay, if observed, would signal physics beyond the Standard Model (SM) that could be discovered at energies significantly lower than
those at which the relevant degrees of freedom could be excited. The black-box theorems \cite{SchechterValle1982,Nieves1984,Takasugi1984,Hirsch2006} would indicate
that the neutrinos are Majorana fermions, and the lepton number is violated in this process by two units.

However, it could be challenging to further use the neutrinoless double-beta decay observations to distinguish between many beyond Standard Model mechanisms that
could contribute to this process \cite{Vergados2012,Horoi2013}. Accurate nuclear structure calculations of the nuclear matrix elements (NME) necessary to analyze the
decay rates could be helpful to narrow down the list of contributing mechanisms and to better identify the more exotic properties of the neutrinos, such as the
existence of the heavy sterile partners that could interact through right-handed currents \cite{KeungSenjanovic1983,Barry2013,Deppisch2016}. The NME for the standard
mass mechanism were thoroughly investigated using several nuclear structure models. Figure 13 of Ref. \cite{NeacsuHoroi2015}  shows some of these NME for isotopes of
immediate experimental relevance. Here, we describe the status of the  shell model calculations of these NME
\cite{Horoi2013,NeacsuHoroi2015,BrownHoroiSenkov2014,SenkovHoroi2014,SenkovHoroiBrown2014,SenkovHoroi2013,HoroiBrown2013,NeacsuStoicaHoroi2012,HoroiStoica2010,HoroiStoicaBrown2007}
and their relevance for discriminating possible competing mechanisms that may contribute to the neutrinoless double-beta decay process.

One possible alternative/competing mechanism considers the contribution from the exchange of the heavy, mostly sterile,
neutrinos \cite{KeungSenjanovic1983,Barry2013,Deppisch2016}. The exchange of left-handed heavy neutrinos is shown to be negligible in most
cases \cite{Mitra2012,Blennow2010}. The exchange of the right-handed heavy neutrinos is predicted by left-right symmetric
models \cite{PatiSalam1974,MohapatraPati1975,Senjanovic1975,KeungSenjanovic1983,Barry2013}, which are presently under active investigation at
LHC \cite{CMS2014,Deppisch2016}. In either case, the same heavy neutrino-exchange NME are necessary for the analysis of the data. For example, considering only the
competition between the light left-handed neutrino-exchange mechanism and the heavy right-handed neutrino-exchange mechanism, one could identify the dominant effect
using half-lives of several isotopes, such as $^{76}$Ge and $^{136}$Xe \cite{Faessler2011}. Some of these heavy neutrino-exchange NME for isotopes of immediate
experimental relevance are shown in Fig. 14 of Ref. \cite{NeacsuHoroi2015}. The range of these matrix elements is quite large due to their sensibility to the
short-range correlation effects that were not treated consistently. One important improvement of these calculations would be obtaining an effective transition
operator that takes into account consistently the short-range correlation effects and the effects of the missing single particle orbits from the model space \cite{HoltEngel2013}.

Some other low-energy effects of the left-right symmetric models, such as those due to the so called $\lambda$ and $\eta$ mechanisms \cite{Doi1985,Barry2013},
could be identified experimentally if one could measure the angular and the energy distribution of the emitted electrons \cite{snemo2010}, but the analysis requires knowledge of additional NME that one can calculate.
Finally, some more exotic possibilities \cite{Vergados2012,Prezeau2003} leading to one- and two-pion exchange NME \cite{Gehman2007} were also calculated in the past within
the interacting shell model approach \cite{Horoi2013,HoroiBrown2013}, and quasiparticle random phase approximation (QRPA) (see, e.g., Ref. \cite{Vergados2012} and references
therein). A more general approach that includes a complete set of dimension six and dimension nine operators to the SM Lagrangian, as well as R-parity violating SUSY contributions, Kaluza-Klein modes in higher dimensions \cite{Bhattacharyya2003,Deppisch2007}, violation of Lorentz invariance and equivalence principle \cite{Leung2000,Klapdor1999,Barenboim2002}, is given in Refs. \cite{Pas1999,Deppisch2012}. Information from double-beta decay can help constrain these contributions, but additional information from the colliders is needed for a full analysis.

In this paper, we consider the possibility of disentangling the contributions of the right-handed currents to the neutrinoless double-beta decay process.
Our analysis mostly focuses on the information one can get from the two-electron energy and angular distributions, which could be used to distinguish contributions
coming from the $\lambda$ and $\eta$ mechanisms from those of the usual light neutrino-exchange mechanism. The analysis is done for $^{82}$Se, which was chosen as a
baseline isotope by the SuperNEMO experiment \cite{snemo2010,nemo32014}. During the preparation of this manuscript, we also found a more general analysis of the terms
contributing to the angular and energy distributions for most of the double-beta decay isotopes based on improved phase space factors and QRPA NME \cite{Stefanik2015}.
Efforts of separating these effects are not new (see, e.g., Refs. \cite{Doi1983,TOMODA1986,Hirsch1994,PhysRevC.64.035501,Bilenky2004} among others).
Our analysis is however more detailed and more specific to the decay of the $^{82}$Se isotope. It considers the competitions between the mass mechanisms and the
heavy right-handed neutrino-exchange mechanism if the contributions from $\lambda$ and $\eta$ mechanisms are ruled out by the two-electron angular and energy distributions.

The paper is organized as follows: Section II presents the general formalism used to describe the neutrinoless double-beta decay under the assumption that the right-handed
currents would contribute. Section III describes the associated two-electron angular and energy distributions. Section IV analyzes the two-electron angular and energy
distributions for different scenarios that consider different relative magnitudes of the $\lambda$ and $\eta$ mechanism amplitudes (please notice the changes of notation).
Section V considers the possibility of disentangling the mass mechanisms from the heavy right-handed neutrino-exchange mechanism, if the $\lambda$ and $\eta$ contributions
could be ruled out by the two-electron energy and angular distributions. Section VI is devoted to conclusions, and Appendixes A, B, and C present detailed formulas used in the formalism.

\section{$0\nu\beta\beta$ decay formalism}\label{formalism}

If right-handed currents exist there are several possible contributions to the neutrinoless double-beta decay rate \cite{Doi1983,Doi1985}. Usually, only the light left-handed neutrino-exchange mechanism (a.k.a. the mass mechanism) is taken
into consideration, but other mechanisms could play a significant role \cite{Vergados2012}. One popular model that considers the right-handed currents contributions is the left-right symmetric model \cite{MohapatraPati1975,Senjanovic1975}, which assumes the existence of heavy particles that are not part of the Standard Model (see also Ref. \cite{Barry2013} for a review specific to double-beta decay).

In the framework of the left-right symmetric model one can write the electron neutrino fields (see Appendix A where we use the notations of Ref. \cite{Barry2013}) as

\begin{eqnarray}
\label{nfields}
\nonumber \nu\sp{\prime}_{eL}&=&\sum_{k}^{light} U_{ek}\nu_{kL}+\sum_k^{heavy}S_{ek} N^c_{kR},\\
\nu\sp{\prime}_{eR}&=&\sum_{k}^{light} T^*_{ek}\nu^c_{iL}+\sum_k^{heavy}V^*_{ek} N_{kR},
\end{eqnarray}
where $\nu\sp{\prime}$ represent flavor states, $\nu$ and $N$ represent mass eigenstates, $U$ and $V$ mixing matrices are almost unitary, while $S$ and $T$ mixing matrices are small.
The $\nu\sp{\prime}_{eL}$ electron neutrino is active for the $V-A$ weak interaction and sterile for the $V+A$ interaction, with the opposite being true for $\nu\sp{\prime}_{eR}$.
Then, the neutrinoless half-life  expression is given by

\begin{eqnarray}
\label{flifetime}
\nonumber \left[ T^{0\nu}_{1/2} \right] ^{-1}  =  G^{0\nu}_{01} g^4_A & \mid & M^{0\nu}\eta_{\nu} +M^{0N}\left(\eta^L_{N_R}+\eta^R_{N_R}\right) \\
 & & +\eta_{\lambda}X_{\lambda}+\eta_{\eta}X_{\eta}+\cdots \mid ^2  ,
\end{eqnarray}
where $\eta_{\nu}$, $\eta^L_{N_R}$, $\eta^R_{N_R}$, $\eta_{\lambda}$, and $\eta_{\eta}$ are neutrino physics parameters defined in Ref. \cite{Barry2013}.
See Appendix A for the definition of the neutrino physics parameters. One should mention that our $\eta_{\lambda}$ and $\eta_{\eta}$ parameters correspond to $\lambda$
and $\eta$ of Ref. \cite{snemo2010}. Above, $M^{0\nu}$  and $M^{0N}$ are the light and heavy neutrino-exchange nuclear matrix elements \cite{Horoi2013,SenkovHoroiBrown2014,Vergados2012} (see their explicit decomposition in Appendix B), and $X_{\lambda}$ and $X_{\eta}$ represent combinations of NME and phase space factors that are analyzed below. Here, $G_{01}^{0\nu}$ is a phase space factor \cite{SuhonenCivitarese1998} that can be calculated with relatively good precision in most cases \cite{Kotila2012,StoicaMirea2013}, and $g_A=1.27$ (see also Appendix C). The ``$\cdots $'' sign stands for other possible contributions, such as those of R-parity violating SUSY particle exchange \cite{Vergados2012,Horoi2013}, Kaluza-Klein modes \cite{Bhattacharyya2003,Deppisch2007,Horoi2013}, violation of Lorentz invariance, equivalence principle \cite{Leung2000,Klapdor1999,Barenboim2002},etc, which are neglected here.

The $\eta^L_{N_R}$ term also exists in the seesaw type I mechanisms, but its contribution is negligible if the heavy mass eigenstates are larger than 1 GeV \cite{Blennow2010}. Assuming a seesaw type I dominance \cite{DevMitra2015}, we neglect it here. If the $\eta_{\lambda}$ and $\eta_{\eta}$ contributions could be ruled out by the two-electron energy and angular distributions, the remaining $\eta_{\nu}$ and $\eta^R_{N_R}$ terms have a very small interference contribution (the interference term is at most 8\% of the two terms in the parenthesis of Eq. \ref{hlifetime} \cite{Halprin1983,Faessler2011}), and the half-life becomes

\begin{flalign} \label{hlifetime}
\left[ T^{0\nu}_{1/2} \right] ^{-1}  =  G^{0\nu}_{01} g^4_A  \left( \left| M^{0\nu}\right|^2 \left| \eta_{\nu} \right|^2 + \left| M^{0N} \right|^2 \left| \eta^R_{N_R}\right|^2 \right). & &
\end{flalign}

Then, the relative contribution of the $\eta_{\nu}$ and $\eta^R_{N_R}$ can be gauged out if one measures the half-life of at least two isotopes \cite{Faessler2011,Vergados2012}, provided that the corresponding matrix elements $M^{0\nu}$ and $M^{0N}$ are known with good precision (see Sec. \ref{heavy} below). These matrix elements were calculated using several methods including the interacting shell model (ISM) \cite{Blennow2010,Horoi2013,HoroiBrown2013,SenkovHoroiBrown2014,SenkovHoroi2013,BrownHoroiSenkov2014,NeacsuHoroi2015} (see Ref. \cite{NeacsuHoroi2015} for a review), quasiparticle random phase approximation (QRPA) \cite{Vergados2012,Suhonen2015}, and interacting boson model (IBM) \cite{Barea2015}. In general, the ISM  results for $M^{0\nu}$ are quite close one to another but smaller than the QRPA and IBM results; the ISM and IBM results for $M^{0N}$ are close, while they are both smaller than the QRPA results. An explanation of this behavior was recently provided \cite{BrownFangHoroi2015}, which suggests a path for improving  these NME. We believe that nuclear shell model matrix elements are the most reliable because they take into consideration all correlations around the Fermi surface, respect all symmetries, and take into account consistently the effects of the missing single particle space via many-body perturbation theory (shown to be small, about 20\%,  for $^{82}$Se \cite{HoltEngel2013}). Because of that, we use no quenching for the bare $0\nu\beta\beta$ operator in our calculations. This conclusion is different from that for the simple Gamow-Teller operator used in single beta and $2\nu\beta\beta$ decays for which a quenching factor of about 0.7 is necessary \cite{BrownFangHoroi2015}.

In what follows, we provide an analysis of the two-electron relative energy and angular distributions using shell model NME. This analysis could be used to analyze data that may be provided by the SuperNEMO experiment to identify the relative contributions of $\eta_{\lambda}$ and $\eta_{\eta}$ terms in Eq. (\ref{flifetime}). A similar analysis using QRPA NME was given in Ref. \cite{snemo2010}. During the preparation of this manuscript, we also found a more general analysis of the terms contributing to the angular and energy distributions, for most of the double-beta decay isotopes, based on improved phase space factors and QRPA NME \cite{Stefanik2015}. However, our analysis is more detailed and more specific to the decay of the $^{82}$Se isotope. The starting point is provided by the classic paper of Doi, Kotani, and Tagasuki \cite{Doi1985}, which describes the neutrinoless double-beta decay process using a low-energy Hamiltonian that includes the effects of the right-handed currents. The $\eta_{\lambda}$ and $\eta_{\eta}$ terms in Eq. (\ref{flifetime}) are related to the $\lambda$ and $\eta$ terms in Ref. \cite{Doi1985}. With some simplifying notations the half-life expression \cite{Doi1985} (here, we omit the contribution from the $\eta^L_{N_R}$ term, which has the same energy and angular distribution as the $\eta_{\nu}$ term) is given by

\begin{eqnarray}
\label{lifetime}
\nonumber \left[ T^{0\nu}_{1/2} \right] ^{-1}&=&\left|M_{GT}^{0\nu}\right| ^2 \left\{ C_{\nu^2} + C_{\nu\lambda}\textmd{cos}\phi_1 + C_{\nu\eta}\textmd{cos}\phi_2 \right.  \\
  &+& \left. C_{\lambda^2} + C_{\eta^2} +C_{\lambda\eta}\textmd{cos}(\phi_1 - \phi_2) \right\} ,
\end{eqnarray}
where $\phi_1$ and $\phi_2$ are the relative $CP$-violating phases (\ref{phases}), and $M_{GT}^{0\nu}$ is the Gamow-Teller contribution of the light neutrino-exchange NME.
Different processes give rise to several contributions: $C_{\nu^2}$ are from the left-handed leptonic and currents, $C_{\lambda^2}$ from the right-handed leptonic and right-handed hadronic currents, and $C_{\eta^2}$ from the right-handed
 leptonic and left-handed hadronic currents. Interference between these terms is represented by the the contributions of
 $C_{\nu\lambda}$, $C_{\nu\eta}$ and $C_{\lambda\eta}$. The precise definitions are
\begin{eqnarray} \label{c-mechanism}
\nonumber C_{\nu^2}	&= C_1 \left< \nu\right> ^2, C_{\nu\lambda}	=& C_2\left< \nu\right>\left< \lambda\right>, 	C_{\nu\eta}	= C_3\left< \eta \right>\left< \nu\right>, \\
      C_{\lambda^2}	&= C_4\left< \lambda\right>^2, C_{\eta^2}	=& C_5\left< \eta \right>^2, 	\ \ \		C_{\lambda\eta}	= C_6\left< \eta \right>\left< \lambda\right> ,
\end{eqnarray}
where $C_{1-6}$ are combinations of nuclear matrix elements and phase-space factors (PSF).
Their expressions can be found in Appendix B, Eqs. (\ref{ci-uri}). Here, $M_{GT}^{0\nu}$ and the
other nuclear matrix elements that appear in the expressions of the $C$ factors are presented in Eq. (\ref{nme-gt}). In the context of the left-right symmetric model, we associate the neutrino physics parameters $\left< \nu \right>$, $\left< \lambda \right>$, and $\left< \eta \right>$ with the corresponding $\eta_i$ parameters defined in Appendix A,
\begin{subequations}\label{mass-parameters}
\begin{align}
\left< \nu \right>	& = \left| \eta_{\nu} \right|\ ,\\\
\left< \lambda \right>	& = \left| \eta_{\lambda} \right|\ ,\\
\left< \eta \right>	& = \left| \eta_{\eta} \right|\ ,
\end{align}
\end{subequations}
but we leave them in this generic form for the case that other mechanisms could contribute. For example, any contribution from a mechanism whose amplitude is proportional with $\sqrt{G^{0\nu}_{01}}$, such as $\eta^L_{N_R}$ and $\eta^R_{N_R}$, may be added to the $\left< \nu \right>$ term with an appropriate redefinition of the nuclear matrix elements and the interference phases.

\section{$0\nu\beta\beta$ decay electrons distributions}

The differential decay rate of the $0^+\rightarrow0^+$ $0\nu\beta\beta$ transition can be expressed as:
\begin{equation}\label{diff-rate}
\frac{\textmd{d}^2W_{0^+\rightarrow0^+}^{0\nu}}{\textmd{d}\epsilon_1 \textmd{d}\text {cos}\theta_{12}} = \frac{a_{0\nu} \omega_{0\nu}(\epsilon_1)}{2\left( m_eR \right)^2} \left[A(\epsilon_1)+B(\epsilon_1)\text {cos}\theta_{12} \right]  .
\end{equation}
Here, $\epsilon_1$ is the energy of one electron in units of $m_e c^2$, $R$ is the nuclear radius ($R=r_0 A^{1/3}$, with $r_0=1.2$fm), $\theta_{12}$ is the angle between the outgoing electrons, and the expressions for the constant $a_{0\nu}$ and the function $\omega_{0\nu}$ are
given in the Appendix C, Eqs. (\ref{a0}) and (\ref{omega0}), respectively.
The functions $A(\epsilon)$ and $B(\epsilon)$ are defined as combinations of factors that include PSF and NME:
\begin{subequations}\label{ab}
\begin{align}
 A(\epsilon_1)&=|N_1(\epsilon_1)|^2+|N_2(\epsilon_1)|^2+|N_3(\epsilon_1)|^2+|N_4(\epsilon_1)|^2,  \\
 B(\epsilon_1)&=-2\text{Re}\left[ N_1^\star(\epsilon_1) N_2(\epsilon_1)+N_3^\star(\epsilon_1) N_4(\epsilon_1) \right].
\end{align}
 \end{subequations}
The detailed expressions of the $N_{1-4}(\epsilon_1)$ components are presented in Eqs. (\ref{n-uri}).

The expression of the half-life can be written as follows:
\begin{eqnarray} \label{half-life}
\nonumber \left[ T_{1/2}^{0\nu} \right]^{-1} &=& \frac{1}{\text{ln2}}\int \textmd{d}W_{0^+\rightarrow0^+}^{0\nu} =  \frac{a_{0\nu}}{\text{ln2} \left( m_eR \right)^2}\\
&\times& \int_1^{T+1} A(\epsilon_1) \omega_{0\nu}(\epsilon_1)\textmd{d}\epsilon_1,
\end{eqnarray}
with the kinetic energy T defined as
\begin{equation}\label{t-energy}
 T=\frac{Q_{\beta\beta}}{m_e c^2}.
 \end{equation}

 \subsection{Angular distributions}

The integration of Eq. (\ref{diff-rate}) over $\epsilon_1$ provides the angular distribution of the electrons.
We can now write it as
\begin{eqnarray}
 \nonumber \frac{\textmd{d}W_{0^+\rightarrow0^+}^{0\nu}}{\textmd{d}\Omega}&=&\frac{a_{0\nu}}{4\pi \left( m_eR \right)^2}\left[
 \int_1^{T+1} A(\epsilon_1)\omega_{0\nu}(\epsilon_1)\textmd{d}\epsilon_1 \right. \\
 &+& \left. \frac{\textmd{d}\Omega}{2\pi} \int_1^{T+1} B(\epsilon_1)\omega_{0\nu}(\epsilon_1)\textmd{d}\epsilon_1 \right],
\end{eqnarray}
where $d\Omega=2\pi d\text {cos}\theta_{12}$.

\subsection{Energy distributions}
Integrating Eq. (\ref{diff-rate}) over cos$\theta_{12}$, one obtains the single electron spectrum.
When investigating the energy distribution, it is convenient to express the decay rate as a function of
the difference in the energy of the two outgoing electrons, $\Delta t=(\epsilon_1 - \epsilon_2 )m_e c^2$, where
$ \epsilon_2=T+2-\epsilon_1$ is the kinetic energy of the second electron.
We now express the energy of one electron as
\begin{equation}
\epsilon_1=\frac{T+2+\frac{\Delta t}{m_e c^2}}{2}.
\end{equation}
After changing the variable, the energy distribution as a function of $\Delta t$ is
\begin{equation}
 \frac{2\textmd{d}W_{0^+\rightarrow0^+}^{0\nu}}{\textmd{d}(\Delta t)}=\frac{2a_{0\nu}}{\left( m_eR \right)^2}
 \frac{\omega_{0\nu}(\Delta t)}{m_e c^2} A(\Delta t).
\end{equation}

\begin{figure}[htb]
\includegraphics[width=0.98\linewidth]{case1}
\caption{Electrons angular distribution (upper panel) and energy distributions (lower panel) for the competition between $\nu$ and $\eta$ mechanisms, Case 1 (see Sec. IV for a full description of the bands).}
\label{eta}
\end{figure}

\begin{figure}[htb]
\includegraphics[width=0.98\linewidth]{case2}
\caption{Same as Fig. \ref{eta} for the competition between $\nu$ and $\lambda$ mechanisms, Case 2.}\label{lambda}
\end{figure}

\section{Results}
Here, we analyze in detail the two-electron angular and energy distributions for $^{82}$Se, which was chosen as a baseline isotope by the SuperNEMO experiment \cite{snemo2010,nemo32014}.
We calculate the $^{82}$Se NME of Eq. (\ref{nme-gt}) using a shell model approach with the JUN45 \cite{JUN45} effective Hamiltonian
in the $jj44$ model space \cite{SenkovHoroiBrown2014,SenkovHoroi2014}. The nuclear structure effects are taken into account by the inclusion of short-range correlations with CD-Bonn
parametrization, finite nucleon size effects, and higher order corrections of the nucleon current \cite{HoroiStoica2010}.
We point out that some of the neutrino potentials in Eq. (\ref{potentials}) are divergent \cite{Doi1985}, such that
the approximations $\chi_{GT\omega}=2-\chi_{GTq}$ and $\chi_{F\omega}=2\chi_F-\chi_{Fq}$ \cite{Tomoda1991} are not accurate.
This simplification was widely used because of the high complexity and difficulty of the previous shell model calculations with large model spaces \cite{Retamosa1995,Caurier1996} when most of $0\nu\beta\beta$ decaying isotopes were considered.
A solution to this problem is to first perform the radial integral over the coordinate space and only after the second integral over the momentum space in Eq. (\ref{i-alpha}).
For $g_A$ we use the older value of 1.254 for an easier comparison to other NME and PSF results in the literature. It was shown in Ref.
\cite{SenkovHoroiBrown2014} that changing to the newer value of 1.27 \cite{pdg-2014} changes the result by only 0.5\%. Most of uncertainties in the shell model calculations come from different parametrization of the short range correlations, but they are less than 20\% for most of the NME. It is also worth noting that the shell model NME are in general smaller by a factor of 2 than the QRPA NME, but recent work on restoring the broken symmetries in QRPA shows a tendency of reducing the QRPA values towards the shell model ones (see, e.g., Sec. IV.c of Ref. \cite{HoroiNeacsu2016}).

The NME calculated in this work are presented on the first line of Table \ref{tab-nme}. The second line displays the normalized values $\chi_{\alpha}$ ($\alpha=F,GT\omega,F\omega,GTq,Fq,T,R,P$).
\begin{table}[htb]
 \caption{The $^{82}$Se NME corresponding to Eq. (\ref{chi-form}).}
 \begin{tabular}{ccccccccc} \hline \hline \label{tab-nme}
  $M_{GT}$&$M_{F}$&$M_{GT\omega}$&$M_{F\omega}$&$M_{GTq}$&$M_{Fq}$&$M_{T}$&$M_{R}$&$M_{P}$ \\ \hline
   $2.993$&$-0.633$& $2.835$        & $-0.618$      & $3.004$   & $-0.487$ &$0.012$  &$3.252$  &$-1.286$   \\ \hline
	  &$\chi_{F}$&$\chi_{GT\omega}$&$\chi_{F\omega}$&$\chi_{GTq}$&$\chi_{Fq}$&$\chi_{T}$&$\chi_{R}$&$\chi_{P}$ \\ \hline
  	  &$-0.134$    & $0.947$	       &$-0.131$		&$1.003$	     &$-0.103$	 & $0.004$    &$1.086$     & $0.430$ \\ \hline \hline
 \end{tabular} \\
The values of the $\chi_{1\pm}$ and $\chi_{2\pm}$ factors of Eq. (\ref{chi}) are \\
$\chi_{1+}=0.717$, $\chi_{1-}=1.338$, $\chi_{2+}=0.736$, $\chi_{2-}=0.930$. \\
\end{table}

The PSF that enter in the components of Eq. (\ref{lifetime}) are calculated in this work using Eq. (\ref{psfs-form}).
These can be also calculated by a simple manipulation of Eq. (\ref{half-life}), involving $\tilde{A}_{\pm k}$ defined in Appendix B.
Using a new effective method to calculate PSF \cite{HoroiNeacsuPSF2015} in agreement with other recent results, we choose a value of 92 for the effective ``screening factor'' ($S_f$) that changes the charge of the daugther nucleus, $Z_s=\frac{S_f}{100} Z$. Reference \cite{HoroiNeacsuPSF2015} provides a detailed study of the $2\nu\beta\beta$ and $0\nu\beta\beta$ PSF using this method for 11 nuclei.
In the case of $G_1$, we obtain results  which are in good agreement with those of Ref. \cite{Stefanik2015}, having a difference of about 8\%.
The results of Ref. \cite{Stefanik2015} have been obtained more rigorously by solving numerically the Dirac equation and by including the effects of the finite nuclear size and electron screening using a Coulomb potential derived from a realistic proton density distribution in the daughter nucleus.
The largest difference is 15.5\% in the case of $G_8$. The original formalism of Ref. \cite{Doi1985} provides significantly larger differences, of up
to more than 64\% for $G_8$ of $^{82}$Se, and would result in differences in half-lives of over 30\% for Case 4, where all the nine PSF contribute.
However, given the larger uncertainty in the NME \cite{BrownFangHoroi2015}, our approximation is satisfactory and we use it in calculations of the half-lives and of the two-electron angular and energy distributions.

\begin{figure}[htb]
\includegraphics[width=0.98\linewidth]{case3}
\caption{Same as Fig. \ref{eta} for the competition between $\lambda$ and $\eta$ mechanisms, Case 3.}\label{no_mass}
\end{figure}

\begin{figure}[htb]
\includegraphics[width=0.97\linewidth]{case4}
\caption{Same as Fig. \ref{eta} for the competition between $\nu$, $\lambda$ and $\eta$ mechanisms, Case 4.}\label{all_mech}
\end{figure}

\begin{table}[htb]
  \caption{The $^{82}$Se PSF corresponding to Eq.  (\ref{psfs-form}) expressed in $\left[ \textmd{yr}^{-1}\right] $}
  \begin{tabular}{@{}ccccc@{}} \hline \hline \label{tab-psfs}
$G_1\times 10^{14}$	&$G_2\times 10^{14}$	&$G_3\times 10^{14}$	&$G_4\times 10^{15}$	&$G_5\times 10^{13}$ \\ \hline
$2.31$			&$7.93$			&$1.61$			&$4.75$			&$5.33$ \\ \hline
			&$G_6\times 10^{12}$	&$G_7\times 10^{10}$	&$G_8\times 10^{11}$	&$G_9\times 10^{9}$ \\ \hline
			&$4.09$			&$2.97$			&$2.02$			&$1.09$  \\ \hline \hline
 \end{tabular}
\end{table}

In our analysis of the angular and energy distributions we consider five scenarios:
a reference case named ``Case 0'', commonly referred to in the literature as the ``mass mechanism''(displayed with a thick blue line in all the figures);
a case when only the mass mechanism and the $\eta$ mechanism contribute, presented as ``Case 1'';
the scenario when only the mass mechanism and the $\lambda$ mechanism contribute, ``Case 2``;
the case when the mass mechanism does not contribute and we have competition and interference between the $\lambda$ and the $\eta$ mechanisms denoted as ''Case 3``;
and the most complex scenario, ''Case 4``, when there is competition and interference between all the mechanisms.

\begin{table}[htb]
 \caption{The neutrino parameter values chosen for the five cases described in the text.}
 \begin{tabular}{@{}lccc@{}} \hline \hline \label{cases}
		&$\left< \nu\right>$&$\left< \lambda\right>$& $\left< \eta\right>$\\ \hline
Case 0 Blue	&$2\times 10^{-7}$&$0$			&$0$			\\ \hline
Case 1 Red	&$2\times 10^{-7}$&$0$			&$0.5\times 10^{-9}$	\\
Case 1 Green	&$2\times 10^{-7}$&$0$			&$2\times 10^{-9}$	\\\hline
Case 2 Red	&$2\times 10^{-7}$&$0.5\times 10^{-7}$	&$0$			\\
Case 2 Green	&$2\times 10^{-7}$&$2\times 10^{-7}$	&$0$			\\ \hline
Case 3 Red	&$0$		&$0.5\times 10^{-7}$	&$0.5\times 10^{-9}$	\\
Case 3 Green	&$0$		&$2\times 10^{-7}$	&$2\times 10^{-9}$	\\ \hline
Case 4 Red	&$2\times 10^{-7}$&$0.5\times 10^{-7}$	&$0.5\times 10^{-9}$	\\
Case 4 Green	&$2\times 10^{-7}$&$2\times 10^{-7}$	&$2\times 10^{-9}$	\\ \hline \hline
\end{tabular}
\end{table}

The values of the effective parameters for these scenarios are chosen such that they highlight the competition or the dominance
of these mechanisms, taking into account the current experimental limits \cite{Barry2013,Stefanik2015} for the $^{76}$Ge $0\nu\beta\beta$ half-life (see also Appendix A).
They are presented in Table \ref{cases}. In the figures, the red color indicates the lower values for $\lambda$ or $\eta$, while the green color is
used for the higher values.

\begin{figure}[ht!]
\includegraphics[width=0.98\linewidth]{case1ratio}
\caption{The angular correlation coefficient corresponding to Case 1. The meaning of the bands is the same as in Figs. $1-4$.}
\end{figure}

\begin{figure}[ht!]
{\includegraphics[width=0.98\linewidth]{case2ratio}}
\caption{The angular correlation coefficient corresponding to Case 2. The meaning of the bands is the same as in Figs. 1-4.}
\end{figure}

For an easier evaluation of each contribution and the interference effects, we provide in Table \ref{tab-ci} the calculated $C_{i}$ factors ($i=1, \ldots , 6$)
of Eq. (\ref{ci-uri}), together with their effective values from Eqs. (\ref{c-mechanism}), for each particular case.
Due to the large $G_7$,$G_8$, and $G_9$ PSF, the contribution of $C_5$ has a significantly higher magnitude compared to the other factors, such that the calculations are
very sensitive to the $\eta$ mechanism for the present limits of the neutrino physics parameters.

\begin{table*}[htb]
 \caption{The $^{82}$Se $C_{i}$ factors ($i=1, \ldots , 6$) corresponding to Eq.  (\ref{lifetime}) expressed in $\left[ yr^{-1}\right] $.
 We also present the effective values when these factors are multiplied with the neutrino parameters from the four cases discussed}
  \begin{tabular}{lcccccc} \hline \hline  \label{tab-ci}
	    &$C_1$		 &$C_2$			&$C_3$			&$C_4$			&$C_5$			&$C_6$ 			\\ \hline
	    &$2.94\times 10^{-14}$&$-1.46\times 10^{-14}$&$4.75\times 10^{-12}$	&$7.72\times 10^{-14}$	&$1.15\times 10^{-9} $	&$-1.01\times 10^{-13}$	\\ \hline
	    &$C_{\nu^2}$	 &$C_{\nu\lambda}$	&$C_{\nu\eta}$		&$C_{\lambda^2}$	&$C_{\eta^2}$		&$C_{\lambda \eta}$	\\ \hline
Case 0 Blue &$1.18\times 10^{-27}$&$0$			&$0$			&$0$			&$0$			&$0$			\\ \hline
Case 1 Red  &$1.18\times 10^{-27}$&$0$			&$4.75\times 10^{-28}$	&$0$			&$2.86\times 10^{-28}$	&$0$			\\
Case 1 Green&$1.18\times 10^{-27}$&$0$			&$1.90\times 10^{-27}$	&$0$			&$4.58\times 10^{-27}$	&$0$			\\ \hline
Case 2 Red  &$1.18\times 10^{-27}$&$-1.46\times 10^{-28}$&$0$			&$1.93\times 10^{-28}$	&$0$			&$0$			\\
Case 2 Green&$1.18\times 10^{-27}$&$-5.83\times 10^{-28}$&$0$			&$3.09\times 10^{-27}$	&$0$			&$0$			\\ \hline
Case 3 Red  &$0$		 &$0$			&$0$			&$1.93\times 10^{-28}$	&$2.86\times 10^{-28}$	&$-2.53\times 10^{-27}$	\\
Case 3 Green&$0$		 &$0$			&$0$			&$3.09\times 10^{-27}$	&$4.58\times 10^{-27}$	&$-4.04\times 10^{-29}$	\\ \hline
Case 4 Red  &$1.18\times 10^{-27}$&$-1.46\times 10^{-28}$&$4.75\times 10^{-28}$	&$1.93\times 10^{-28}$	&$2.86\times 10^{-28}$	&$-2.53\times 10^{-30}$	\\
Case 4 Green&$1.18\times 10^{-27}$&$-5.83\times 10^{-28}$&$1.90\times 10^{-27}$	&$3.09\times 10^{-27}$	&$4.58\times 10^{-27}$	&$-4.04\times 10^{-29}$	\\ \hline \hline
\end{tabular}
\end{table*}

One may calculate the $0\nu\beta\beta$ half-life with either Eq. (\ref{lifetime}) using the nine PSF of Eq. (\ref{psfs-form}) displayed in Table \ref{tab-psfs} or by integrating Eq. (\ref{diff-rate}) over angles ($\theta_{12}$ from $0$ to $\pi$) and energy  in Eq. (\ref{half-life}) ($\Delta t$ goes from $0$ to $Q_{\beta\beta}$, which is $2.99$ MeV for $^{82}$Se).
The calculated half-lives for the cases of interest are presented in Table \ref{half-lives}. There are four combinations for the $CP$ phases
$\phi_1$ and $\phi_2$, providing up to four values for the half-lives for each case.
All half-lives in Table \ref{half-lives}, except Case 3 Red, are above the present experimental limits, but within the reach of the SuperNEMO experimental setup ($1.0\times 10^{26}$ years).
One should also mention that the on-axis limits for the neutrino physics parameters $<\lambda>$ and $<\eta>$ corresponding to the same half-life, $9.41\times 10^{25}$ years, as the 100 meV mass mechanism are $1.2 \times 10^{-7}$ and $1.0 \times 10^{-9}$, respectively.
The bands in the figures represent the interference
effects of these phases, and their width is the maximum difference between them.
In the case of the mass mechanism, there is no interference, such that Case 0 is represented by a single thick blue line.
This line is present in all the figures to provide the reader with a reference scenario, which is the most studied in the literature.
In the following, we discuss these cases.

\begin{table*}[htb]
 \caption{Calculated half-lives ($T_{1/2}$) for the four possible combinations of values for $\phi_1$ and $\phi_2$ in Eq. (\ref{lifetime}).}
 \begin{tabular}{@{}l|c|c|c|c@{}} \hline  \hline \label{half-lives}
		&$\phi_1=0,\phi_2=0$	&$\phi_1=\pi,\phi_2=\pi$&$\phi_1=0,\phi_2=\pi$	&$\phi_1=\pi,\phi_2=0$	\\ \hline
Case 0 Blue	&$9.41\times 10^{25}$	&$9.41\times 10^{25}$	&$9.41\times 10^{25}$	&$9.41\times 10^{25}$	\\ \hline
Case 1 Red	&$5.72\times 10^{25}$	&$1.12\times 10^{26}$	&$1.12\times 10^{26}$	&$5.72\times 10^{25}$	\\
Case 1 Green	&$1.45\times 10^{25}$	&$2.87\times 10^{25}$	&$2.87\times 10^{25}$	&$1.45\times 10^{25}$	\\\hline
Case 2 Red	&$9.05\times 10^{25}$	&$7.31\times 10^{25}$	&$9.05\times 10^{25}$	&$7.31\times 10^{25}$	\\
Case 2 Green	&$3.01\times 10^{25}$	&$2.29\times 10^{25}$	&$3.01\times 10^{25}$	&$2.29\times 10^{25}$	\\ \hline
Case 3 Red	&$2.32\times 10^{26}$	&$2.32\times 10^{26}$	&$2.30\times 10^{26}$	&$2.30\times 10^{26}$	\\
Case 3 Green	&$1.45\times 10^{25}$	&$1.45\times 10^{25}$	&$1.44\times 10^{25}$	&$1.44\times 10^{25}$	\\ \hline
Case 4 Red	&$5.59\times 10^{25}$	&$8.36\times 10^{25}$	&$1.07\times 10^{26}$	&$4.86\times 10^{25}$	\\
Case 4 Green	&$1.09\times 10^{25}$	&$1.48\times 10^{25}$	&$1.73\times 10^{25}$	&$9.75\times 10^{24}$	\\ \hline \hline
\end{tabular}
\end{table*}

Case 0, representing the mass mechanism and displayed in the Figs. $1-4$ with a blue line, is the most studied mechanism in the literature. The value of the effective neutrino mass parameter $\left< \nu \right> =\left| \eta_{\nu} \right|$ is chosen to correspond to a neutrino mass limit of about 0.1 eV, which results in a calculated half-life of $9.4\times 10^{25}$, just beyond the current experimental limits but within the SuperNEMO reach \cite{nemo32014}. From Figs. $1-2$, one can see that this mode dominates the other contributions as long as $\left< \nu \right> \geq 4 \times \left< \lambda \right>$ and $\left< \nu \right> \geq 400 \times \left< \eta \right>$ (the red bands).
Should any of the $\left< \lambda \right>$ or $\left< \eta \right>$ parameters increase four times (hatched green bands), the distributions change and one
could identify the domination of another mechanism.

\begin{figure}[ht!]
{\includegraphics[width=0.98\linewidth]{case3ratio}}
\caption{The angular correlation coefficient corresponding to Case 3. The meaning of the bands is the same as in Figs. $1-4$. The red and green (narrow) bands are overlapping.}
\end{figure}

\begin{figure}[ht!]
{\includegraphics[width=0.9\linewidth]{case4ratio}}
\caption{The angular correlation coefficient corresponding to Case 4. The meaning of the bands is the same as in Figs. $1-4$.}
\end{figure}

Case 1 presented in Fig. \ref{eta}  describes the $\eta$ mechanism dominance (hatched green bands) showing a significant change in the shape of the angular distribution (Fig. \ref{eta}, upper panel), while the energy distribution retains the shape of Case 0, only increasing in amplitude.
In the scenario of Case 2 presented in Fig. \ref{lambda}, one can see the dominance of the $\lambda$ mechanism (hatched green bands) in both distributions as changes in the shape and amplitude. One can conclude that one can use these different shape changes to distinguish between $\left< \nu \right>$, $\left< \lambda \right>$, and $\left< \eta \right>$ mechanism dominance, assuming that only two of them can compete.

However, one needs to consider the case when the $|m_{ee}|=m_e \left< \nu \right>$ is very small or zero, while the $\lambda$ and $\eta$ mechanisms are competing. This scenario is covered by Case 3 presented in Fig. \ref{no_mass}. The interference term $C_{\lambda \eta}$ is very small leading to very narrow interference bands.
Dominance of any of the two mechanisms would show little difference from the similar behavior shown in Figs. \ref{eta} and \ref{lambda} (the shape is fixed by the small interference term, while in Case 1 and 2 the dependence on the interference phases could distort the shapes).
The green lines in Case 3 are just rescaling of the red to emphasize the effect of rescaling relative to the standard mass mechanism (blue line).
The shapes of the distributions and their changes seem to be similar to some of those in Fig. \ref{lambda}. However, the ratio max/min in the angular distribution (15/1 for Case 3 vs 2/1 for Case 2) could be used to distinguish between these two cases.

Case 4 allows competition between all three contributions (Fig. \ref{all_mech}). Obviously, the qualitative behavior of these distributions cannot be easily disentangled from those of Cases $1-3$ discussed above. That would require a numerical simulation that includes interference effects to rule in or out some of these scenarios.

One should also mention that the energy distribution of the angular correlation coefficient, $\alpha = B(\epsilon)/A(\epsilon)$ in our Eq. (\ref{diff-rate}), could provide additional information (see, e.g., Figs. $6.5 - 6.9$ of \cite{Doi1985} and Fig. 7 of \cite{Stefanik2015}). Figures $5 - 8$ show the angular correlation coefficient $\alpha(\Delta t)$ of all four cases analyzed in Figs. $1 - 4$. One can clearly see that Cases 2 and 3 can also be identified by the value of $\alpha$ when the energies of the two emitted electrons are very close ($\Delta t \approx 0$). Cases 3 and 1 can be separated by the shape of their energy distributions. Figures $5 - 8$ show that the angular correlation coefficient could be also used to better identify the other cases analyzed in Figs. $1 - 4$.

Given the complexity of our analysis, and considering the potential usefulness for future analyses, we provide a link to a Mathematica file that can be used to perform these calculations and produce the plots included in this paper \cite{edistribMN2015}.

\begin{table*}[htb]
 \caption{Calculated limits of half-lives ratios, Eq. (\ref{hlratio}), for different combinations of isotopes (see text for details). For example, in the combination Ge/Se (1) corresponds to Ge and (2) to Se.}
 \begin{tabular}{@{}l|cc|cc|cc|cc|cc|cc@{}}  \hline \hline \label{hlrtable}
 & \multicolumn{2}{c}{Ge/Se} & \multicolumn{2}{|c}{Ge/Te} & \multicolumn{2}{|c}{Ge/Xe} & \multicolumn{2}{|c}{Se/Te} & \multicolumn{2}{|c}{Se/Xe} & \multicolumn{2}{|c}{Te/Xe}  \\
\cline{2-13}
		& Ge & Se & Ge & Te & Ge & Xe & Se & Te & Se & Xe & Te & Xe \\ \hline
$G^{0\nu}_{01}\times10^{14}$ & 0.237 & 1.018 & 0.237 & 1.425 & 0.237 & 1.462 & 1.018 & 1.425 & 1.018 & 1.462 & 1.425 & 1.462 \\
$M^{0\nu}(1/2)$  & 3.57 & 3.39 & 3.57 & 1.93 & 3.57 & 1.76 & 3.39 & 1.93 & 3.39 & 1.76 & 1.93 & 1.76 \\
$M^{0N}(1/2)$  & 202 & 187 & 202 & 136 & 202 & 143 & 187 & 136 & 187 & 143 & 136 & 143 \\
\cline{2-13}
$T_{1/2}^{\nu}(1)/T_{1/2}^{\nu}(2)$ & \multicolumn{2}{c}{3.87} & \multicolumn{2}{|c}{1.76} & \multicolumn{2}{|c}{1.50} & \multicolumn{2}{|c}{0.45} & \multicolumn{2}{|c}{0.39} & \multicolumn{2}{|c}{0.85}  \\
$T_{1/2}^{N}(1)/T_{1/2}^{N}(2)$     & \multicolumn{2}{c}{3.68} & \multicolumn{2}{|c}{2.73} & \multicolumn{2}{|c}{3.09} & \multicolumn{2}{|c}{0.74} & \multicolumn{2}{|c}{0.84} & \multicolumn{2}{|c}{1.13}  \\
$R(N/\nu)$ present & \multicolumn{2}{c}{0.95} & \multicolumn{2}{|c}{1.55} & \multicolumn{2}{|c}{2.06} & \multicolumn{2}{|c}{1.63} & \multicolumn{2}{|c}{2.17} & \multicolumn{2}{|c}{1.33}  \\ \hline
$R(N/\nu)$ \cite{FaesslerGonzales2014} & \multicolumn{2}{c}{1.02} & \multicolumn{2}{|c}{1.39} & \multicolumn{2}{|c}{1.42} & \multicolumn{2}{|c}{1.36} & \multicolumn{2}{|c}{1.39} & \multicolumn{2}{|c}{1.03}  \\
\hline \hline
\end{tabular}
\end{table*}

\section{Disentangling the heavy neutrino contribution}\label{heavy}

As mentioned in Sec. \ref{formalism},
if the $\eta_{\lambda}$ and $\eta_{\eta}$ contributions could be ruled out by the two-electron energy and angular distributions analyzed in the previous section, and in that case assuming a seesaw type I dominance \cite{DevMitra2015} the half-life is given by Eq. (\ref{hlifetime}).
Then, the relative contribution of the $\eta_{\nu}$ and $\eta^R_{N_R}$ terms can be identified if one measures the half-life of at least two isotopes \cite{Faessler2011,Vergados2012}, provided that the corresponding matrix elements $M^{0\nu}$ and $M^{0N}$ are known with good precision.
References \cite{Faessler2011,Vergados2012} already provided some limits of the ratios of the half-lives  of different isotopes based on older QRPA calculations. However, based on those calculations, the two limits for $r(\nu/N)\equiv T_{1/2}^{\nu/N}(1)/T_{1/2}^{\nu/N}(2)$
\begin{equation}
\label{hlratio}
r(\nu/N)=\frac{G^{0\nu}_{01}(2) \left| M^{0\nu/N}(2) \right|^2}{G^{0\nu}_{01}(1) \left| M^{0\nu/N}(1) \right|^2},
\end{equation}
were too close to allow for a good separation of the contribution of these two mechanisms. In Eq. (\ref{hlratio}), terms $(1)$ and $(2)$ designate members of a pair of isotopes. Below, we present the results based on our shell model calculations given in Tables III and IV of Ref. \cite{NeacsuHoroi2015}. In Table \ref{hlrtable},  Ge, Se, Te, and Xe are short-hand notions for $^{76}$Ge, $^{82}$Se, $^{130}$Te, and $^{136}$Xe, respectively. In the table, we only use the NME calculated with CD-Bonn short-range correlations. The $G^{0\nu}_{01}$ factors from Table III of Ref. \cite{Stefanik2015} were used (they are very close to those of Ref. \cite{Mirea2014up}).

The pre-last line in Table \ref{hlrtable} presents the ratio of the ratios of half-lives, $R(N/\nu)=r(N)/r(\nu)$, calculated with our NME. One can see that the largest ratio is obtained for the combination $^{82}$Se/$^{136}$Xe. Its magnitude larger than 2 indicates that one can differentiate between these two limits if the half-lives are known with reasonable uncertainties and provided that the NME can be calculated with sufficient precision. The last line in Table \ref{hlrtable} shows the same quantity calculated with the recent QRPA NME taken from Table I (columns d) of Ref. \cite{FaesslerGonzales2014}. On can see that  these ratios are not as favorable in identifying the two limits. This analysis emphasizes again the need of having reliable NME for all mechanisms.

\section{Conclusions}
In this paper, we calculate nuclear matrix elements, phase-space factors, and half-lives for the  $\ 0\nu\beta\beta \left(0^+ \rightarrow 0^+ \right)$ decay of $^{82}$Se under different scenarios that include, besides the mass mechanism, the mixed right-handed/left-handed currents contributions known as $\eta$ and $\lambda$ mechanisms. For the mass mechanism dominance scenario, the results are consistent with previous calculations \cite{SenkovHoroiBrown2014} using the same Hamiltonian. Inclusion of contributions from $\eta$ and $\lambda$ mechanisms have the tendency to decrease the half-lives.

We present the two-electrons angular and energy distributions for five theoretical scenarios of mixing between mass mechanisms contributions and $\eta$ and $\lambda$ mechanism contributions. From the figures presented in the paper, one can recover the general conclusion \cite{Doi1985} that the energy distribution can be used to distinguish between the mass mechanism and the $\lambda$ mechanism,
while the angular distribution can be used in addition to the energy distribution to distinguish between the mass mechanism and the $\eta$ mechanism, but the identification could be more nuanced due to the lack of knowledge of the interference phases.
In the case of the energy distributions for the mass mechanism dominance (blue line) and the $\lambda$ mechanism dominance (green band in Figure \ref{lambda}, lower panel), we find similar results to those of Fig. 2 in Ref. \cite{snemo2010}.
However, our results emphasize the significant role of the interference phases $\phi_1$ and $\phi_2$ in identifying the effect.

We also find out from the analysis of Case 3 that if the effective neutrino mass is very small, close to zero, and the $\eta$ and $\lambda$ mechanisms are competing, then one can potentially  identify this scenario from the $\lambda $ dominance, Case 2, by comparing the ratio min-to-max in the angular distributions and/or by the behavior of the angular correlation coefficient for almost equal electron energies. The small interference effects in Case 3 could be also used as an additional identification tool. These conclusions seem to be stable even if one considers small NME changes, such as those due to different short-range correlations  models.

We conclude that the $\eta$ mechanism, if it exists, may be favored to compete with the mass mechanisms due to the larger contribution from the phase-space factors. Reference \cite{Barry2013} shows however that it is possible to obtain a $\lambda$ mechanism dominance in some cases.

Finally we show that if the $\eta_{\lambda}$ and $\eta_{\eta}$ contributions could be ruled out by the two-electron energy and angular distributions, the mass mechanisms can be disentangled from the heavy right-handed neutrino-exchange mechanism using ratios of half-lives of few isotopes. The analysis based on our shell model NME indicates that the most favorable combinations of isotopes would be $^{82}$Se/$^{136}$Xe and $^{76}$Ge/$^{136}$Xe.

Certainly, the analysis presented in this paper is based on the positive detection of the neutrinoless double-beta decay, followed by the collection of enough events that one can use to make assessments on the angular and energy distributions. Similar distributions were obtained with high precision by NEMO-3 for the $2\nu\beta\beta$ of $^{100}$Mo, but a very large number, about 1 million, of events were collected \cite{nemo32014}. Clearly, this large number of events will not be available for any $0\nu\beta\beta$ experiment, but we believe that the tools provided by our analysis could help to assess probabilities for these mechanisms even if only tens of events are collected.

\begin{acknowledgments}
Support from the NUCLEI SciDAC Collaboration under U.S. Department of Energy Grants No. DE-SC0008529 and DE-SC0008641 is acknowledged.
M.H. also acknowledges U.S. NSF Grant No. PHY-1404442.
\end{acknowledgments}

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