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Home > Research > connections > Essays > Blue Faience Bowls and Social Practice, by Dr Martin Bommas.
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Blue Faience Bowls and Social Practice: New light on their use and function
In 'Essays'
Blue Faience Bowls and Social Practice, by Dr Martin Bommas.
Communication Through Music, by Eleanor Simmance.
Gestures of Communication, by Emily Millward.
Innovation Through Interactions, by Dr Carla Gallorini.
Intercultural Communication, by Carl Graves.
Petitions to the Divine, by Gabrielle Heffernan.
Scarabs: Appeals for Protection and Resurrection, by Dr Nicola J Adderley.
The Dead and the Living Interacting Through Text, by Valentina Pasquali.
The Lost Art of Egyptian Lithics, by Meagan Mangum.
Visualizing Ideology, by Steven R. W. Gregory
Writing - Image - Material, by Dr Michela Luiselli.
Back to 'connections'
By Dr Martin Bommas
Despite often being displayed prominently in exhibitions on ancient Egyptian minor art, blue faience bowls are among the most famed but also least studied.1 The attention paid to these outstanding artefacts, often inspired by the modern viewers' taste for beauty has unfortunately not translated into an equally intensive scholarly interest in the use, form and function of blue faience bowls in Egypt.2 Apart from later developments in Greco-Roman times, blue faience bowls are of hemispherical shape and show shiny greenish-blue surfaces. Often they have black figurative paintings and in some rare cases inscriptions (fig. 1 © IAA University of Birmingham) while the oldest blue faience bowls often come with rims painted in black (fig. 2). Although for these vessels a number of terms circulate, in most cases based on creativity rather than facts,3 until today the various functions of these bowls both in private and royal contexts (fig. 1) is hardly fully understood. Nevertheless, there seems to be a general agreement on two rather different uses of blue faience bowls at least: first, blue faience bowls were widely used in the cult of Hathor4, secondly they made up part of tomb equipments of wealthy dead individuals from the Middle Kingdom onwards.5 This article aims at broadening the debate and offers some hints on two more uses of blue faience bowls within funerary culture. As will be seen, for both these new categories research into the communication with an addressee who remains passive plays a vital role. With the help of ancient Egyptian texts, the use of blue faience bowls can be assessed in a new way.
Interaction through offering rituals
Funerary rites in ancient Egypt have been the subject of intensive research, especially over the last 20 years with a rediscovery ofthe role of accompanying recitation literature being among the major achievements.6 In addition to rituals within fixed locations in bounded sacred space – such as the Ritual of Opening the Mouth which took place in the open forecourts of tombs - other less stationary rituals underline the more dynamic aspects of ritualistic actions, thus pointing at what can be referred to as rite de passage - such as the so-called Voyage to Sais. In addition to that, a third category includes a series of ritualistic actions that were performed at various stages of the funerary rite – such as the offering ritual which was not limited to one location. Offering rites in front of the dead body lying on its bier included the most developed recitations which aimed at addressing the deceased as Osiris and preparing him to accept offerings for his well being in the netherworld. Here, communication with a mostly passive deceased played a crucial role in enforcing his change of status. There can be no doubt that addressing the dead individual as Osiris NN had to be both formalised and individualised in order to achieve the recipient's attention. Thousands of these glorifications (or Verklärungen in German) are attested in both the mummification ritual and offering rites. Their aim is to negotiate the deceased's netherworldy status in relation to his mythical antecedant Osiris in whose footsteps every dead individual was supposed to follow. Although the majority of the ritualistic actions that led to a successful burial have been investigated in detail, the concluding rites which include the actual interment have not been fully understood.7 Although the evidence is rather patchy for a number of reasons, it seems obvious that the final burial was accompanied by further rituals. Which rituals were performed in detail had in fact to do with the type of architecture chosen to embrace an individual's final resting place: a very elaborate tomb architecture which mushroomed in Thebes for a very short time during the Ramesside Period favoured a sloping passage decending into the burial chamber8 which would not only allow for comfortably pulling down the deceased's coffin to its final destination: also the closest relatives would be in the position to see the dead individual to his burial chamber before its door would close forever. In the tomb of Djehutimes (TT 32), the sloping passage turns 360 degrees through a single turn before descending 30 metres and arriving at the burial chamber, allowing Djehutimes' relatives to say farewell exactly where he was buried.
The other variant which is more commonly attested since the Old Kingdom included a tomb shaft through which the sarcophagi slid into the tomb chamber only secured by long ropes. Steps hewn out at two sides of the shaft allowed those involved to easily climb up or down, as illustrated by an ostracon today kept in the Manchester University Museum (fig. 3). Texts with standard protection songs that accompanied the lowering of the sarcophagus where recited by lector priests from papyrus rolls; one of the books known has the title ''The protection of the gods sorrounds (me)'.9 Where shaft tombs were involved, only a small number of relatives were invited to attend the final ceremonies as is clearly narrated by the ostracon from Manchester. Regardless of which tomb architecture was preferred, the contents of the final burial rites must have been the same, due to the agreed set of ritualist actions. What is certain, however, is that during these final rites objects were laid out before the entrance into the burial chamber and recitations took place, thus marking the tomb as an interface for the dead between this world and the beyond. This procedure was probably the quitest part of the funeral with no wailing women and villagers around to produce the noise that was needed during the procession to ward off Seth, the dead individual's mythical enemy. Because the actual interment of the deceased did not form part of the funeral processions, the intimacy of this ritual was hardly ever focussed on: tomb depictions never display these actions because they were considered private.
Lamentations as farewell address
In-depth research has recently shown that the final rites at the entrance of shaft tombs must have been accompanied by a number of rituals carried out in the open. These rites included the deposit of vessels10 that contained food offerings11 as a token of a final farewell before the tomb shaft was closed forever. It is here that the so-called lamentations of Isis and Nephthys have their Sitz im Leben (place in life). Lamentations form a group of texts in their own right and are only peripherally linked with glorifications. They have mainly been studied without taking the archaeological evidence into account, or in other words: scholars who studied the archaeological remains have not made the link with the accompanying texts and those studying the texts did not show an interest in manual rites. That the two belong together, and both physical enactment and recital are in fact intrinsically tied together is made clear by the closing passage from Papyrus Berlin 3008 from the Ptolemaic Period. Here, a manual gives detailed instructions how the lamentations were to be performed:
Now when reciting this, the place should be totally secluded, without it being witnessed or heard by any eyes except for the chief lector priest and the sem–priest.
Then one should bring two women with comely forms. Cause them to sit upon the ground in the first portal of the hall of appearance. Inscribe their arms with the names of Isis and Nephthys. Place vessels of faience filled with water in their right hands, and cakes made in White Walls (i.e. Memphis, author's note) in their left hands. Cause their faces to be lowered. To be done at the third hour in the day, likewise at the eighth hour of the day. You should not weary of reciting this book at the hour of festival.
It has come to an end.12
This passage is one of the few occasions where manual rites are mentioned within lamentations. Moreover it presents its modern readers with the context in which the lamentations were recited. Nevertheless, these instructions were never studied with regard to the actual context of performance13 which – as the text itself points out – is the receipt of offerings.
The use of faience bowls during the final offering ritual
As it further appears from this passage, faience bowls – and one should probably assume that blue faience bowls are meant here14 – play an important role in the final stages of the burial rite, presented by two women playing the divine roles of Isis and Nephthys as illustrated on the ostracon from Manchester (fig. 3). How exactly these faience bowls had to look is impossible to determine today: various different forms are attested in Ptolemaic times15, among them drinking cups16 but also flat bowls which became wide spread in Roman Times (fig. 4)17. It is important to note that this scene does not include the wailing with which Isis and Nephthys are often linked (fig. 5)18. While wailing involves one hand being raised19, Papyrus Berlin 3008 leaves no doubt that here, both goddesses are shown offering bread and water and are, therefore, not mourning. With the beginning of the final offering rite employing blue faience bowls, mourning has come to an end.
Blue faience bowls were obviously not mere containers for food or water that were offered silently. Recitations that made part of deposit rites are well attested from within the cult of Hathor where faience bowls were the most common type of vessels found, usually carrying a simple lotus pattern20: Stelae erected by turquoise mining expeditions at Serabit el-Khadim during the MK preserve prayers to the goddess Hathor to protect the group.21 Although no reference seems to be made to the use of blue faience bowls, water presented in drinking cups often fulfilled the function of an intermediary between the living and the world beyond.22 Contact with the sacred was usually made through the use of water, the drinking of which would allow a text or a spoken prayer to be consumed by a god or a dead individual in his capacity of a glorified spirit. The greenish-blue colour as well as nilotic motifs often depicted on the insides of these bowls suggests ideas of rejuvenation and the abundance of funerary provisions.23
It becomes evident from Papyrus Berlin 3008 that in addition to the use of blue faience bowls within the cult of Hathor and as part of funerary equipments, a communicative use of bowls is attested in a context where immediate and also intimate connection was made with a dead loved one at the end of the burial rite. Which songs were sung is laid out in detail by the lamentations of Isis and Nephthys, but the contents of drinking cups were presented non-verbally: verbal communication rested exclusively on the texts as mythical interpretation of the manual offering rite and needed no further recitations.
Faience bowls used on Rememberance Day
From here, it is only a short leap to a fourth category of use for blue faience bowls: during the funerary festivals when the living met with the dead in their tomb forecourts for festive eating and drinking24, drinking cups and lotus chalices25 were widely used in a context where re-enforcing the dead individual's rejuvenation was on the agenda. This approach, attested since the Old Kingdom,26 focused on the re-establishment of close links between the worlds of the living and the dead within sacred space. Shaping identity with the help of religious festivals is one of the key aspects in creating communitas, to use a term coined by Victor Turner27: festivals are, among others functions, platforms for remembering the dead and therefore to be regarded as the locus classicus in forming cultural memory.28
In Egypt, cultural identity was shaped by remembering the dead. Although fragmented, shrine 11 at Gebel es-Silsilah has a depiction of such a festival scene: in front of the deceased and his wife an offering table is mounted. One man and two scantily clad girls are playing music and dance while three other men are sat on the ground and clap their hands. The text they perform is in fact a sacred song, deeply rooted in Personal Religion:29 'Your lord is Amun/ good father/ lord of the entire land/ You are a protector and we are afraid of no-one/ Sweet father, lord of the entire land (...).' The scene is observed by four men sitting on stools, holding lotus flowers in their right hands. Without any doubt, this is the context in which the wishes for a dead individual's rejuvenation are renewed. It is here where good times are celebrated, the living communicate with the dead and rejuvenating water is drunk from blue faience bowls that are covered with lotus flowers. But it is also the context in which personal religious beliefs were practised, since the wider context in which contact with dead relatives was made possible was the 'Beautiful Festival of the Valley'. Here, the Theban god Amun visited the tombs and temples of deceased gods, kings and private people to reinforce relations with all those who inhabited the tripartite world consisting of sky, earth and necropolis.30 It seems that in such festive practices blue faience bowls served the needs of all those who fell into one (or two) of these categories, enabling the communication between the living and the dead.
E.g. Dunn Friedman 1998; Cubet and Pierret-Bonnefois 2005.
One of the early publications is Krönig 1934. To date, the only monographic approach to this topic is Strauss 1974. Prompted from a master's thesis, it is probably fair to say that this publication hampered the research on blue faience bowls rather than furthering it.
Strauss 1974 calls these bowls "Nunschalen" (linking the vessels with Nun, the Egyptian term for primeval waters); Pinch 1994: 312-313 uses the term "marsh bowls" referring to the 'life-giving properties of the inundation'.
See Pinch 1993.
During the Middle Kingdom, blue faience bowls increasingly formed part of funerary equipments such as in Beni Hassan (Garstang 1907: 142, fig. 140) or Hu (Nicholson 1993: 25 and 27, fig. 17). A shallow bowl, probably coming from el-Matariya and dating to Dyn. 12-13, contained model fruits and vegetables, see Dunn Friedman 1998:151 and 239.
Assmann 2002-2008.
The most recent article on this topic does not discuss the rites following on from the Ritual of Opening the Mouth, i.e. the offering ritual, interment of the body and concluding rituals (Hayes 2010: 8).
Assmann 2003: 50-51.
Altenmüller 1975: 762.
Seiler 2005: 40-52 differentiates between 'Beigabenkeramik' as deposited as part of the funerary equipment and 'Kultkeramik' which was used in publicly accessible spaces at the entrances of tombs.
Winlock 1923: 38.
Trans. Smith 2009: 133-134.
Recent studies include Lichtheim 1980: 120; Smith 2009: 133-134; Kucharek 2010: 94-96.
On individual colours of faience see Kaczmarczyk and Hedges 1983: 140-184.
See for an overview of shapes the catalogue of faience vessels in the Greco-Roman Museum in Alexandria, Nenna and Seif-el Din 2000.
Nenna and Seif-el Din 2000: Pl. 1-5.
Nenna and Seif-el Din 2000: 311-318.
See Millward's article in this collection.
See ECM148 in the contribution by E. Millward to this project.
Pinch 1993: 308.
Clear evidence is presented by drinking cups that were inscribed with letters to the dead and deposited in tombs, see Bommas 1993.
A blue faience bowl with a greenish colour and a black rim from the Louvre (Ae E 10909, Cubet and Pierret-Bonnefois 2005: 40) dating to the Late Middle Kingdom and Second Intermediate Period shows among floral patterns fish and birds flapping in the marshes.
Bommas 2010: 170-172. For the reference to the cult of Hathor see Schott 1952: 77-78.
See Schott 1952: 77 for a similar cup depicted in Tomb TT 181.
Seiler 2005: 180.
Turner 2008: 94-130.
Assmann 1991: 15; Beck and Wiemer 2009.
For a song attested in shrine 11 at Gebel es-Silsileh see recently Luiselli 2011: 327-328 (with older literature).
Bommas 2005.
Altenmüller, H., 1975. 'Bestattungsritual', in: W. Helck and E. Otto (eds.), Lexikon der Ägyptologie I, Wiesbaden, sp. 745-765.
Assmann, J., 1991. 'Der zweidimensionale Mensch: das Fest als Medium des kollektiven Gedächtnises', in: J. Assmann and T. Sundermeier (eds.), Das Fest und das Heilige. Religiöse Kontrapunkte zur Alltagswelt. Studien zum verstehen fremder Religionen I, Gütersloh, 13-30.
Assmann, J., 2002-2008. Altägyptische Totenliturgien I-III. Heidelberg.
Assmann, J., 2003. 'The Ramesside tomb and the construction of sacred space', in: N. Strudwick and J. Taylor (eds.), The Theban Necorpolis. Past, Present and Future, London, 46-52.
Beck, H. and H.-U. Wiemer, 2009. 'Feiern und Erinnern – eine Einleitung', in: H. Beck und H.-U. Wiemer (eds.), Feiern und Erinnern. Geschichtsbilder im Spiegel antiker Feste. Stidien zur Alten Geschichte 12, Berlin, 9-54 .
Bommas, M., 1993. 'Zur Datierung einiger Briefe an die Toten', in: Göttinger Miszellen 173, 53-60.
Bommas, M., 2005. 'Situlae and the Offering of Water in the Divine Funerary Cult: A New Approach to the Ritual of Djeme', in: A. Amenta/M. Luiselli/M.N. Sordi (ed.), L'acqua nell' antico Egitto, Proceedings of the First International Conference for Young Egyptologists, 15th-18th of October 2003 in Chianciano Terme, Rome, 257-272.
Bommas, M., 2010. 'The mechanics of social connections between the living and the dead in ancient Egypt', in: M. Carroll and J. Rempel (eds.), Living Through the Dead: Burial, Commemoration in the Classical World, Oxford, 159-182.
Cubet, A. and G. Pierret-Bonnefois, 2005. Faïence de l'Antiquité de l'Égypte à l'Iran. Paris.
Dunn Friedman, F. 1998. Gifts of the Nile. Ancient Egyptian Faience. London.
Strauss, E.-C., 1974. Die Nunschale – Eine Gefässgruppe des Neuen Reiches, Münchner Ägyptologische Studien 30. Berlin.
Garstang, J., 1907. The Burial Customs of Ancient Egypt, as illustrated by tombs of the Middle Kingdom, being a report of excavations made in the Necropolis of Beni Hassan during 1902-3-4. London.
Hays, H., 2010. 'Funerary Rituals (Pharaonic Period)' in: J. Dieleman and W. Wendrich (eds.), UCLA Encyclopedia of Egyptology, Los Angeles, 1-15 (http://escholarship.org/uc/item/1r32g9zn, last accessed 16.2.2012).
Krönig, W., 1934. 'Ägyptische Faience-Schalen des Neuen Reiches. Eine motivgeschichtliche Untersuchung', MDAIK 5, 144-166.
Kaczmarczyk, A. and R.E.M. Hedges, 1983. Ancient Egyptian Faience. An analytical survey of Egyptian Faience from Predynastic to Roman Times. London.
Kucharek, A., 2010. Die Klagelieder von Isis und Nephthys in Texten der Griechisch-Römischen Zeit. Heidelberg.
Lichtheim, M., 1980. Ancient Egyptian Literature III. Berkeley/Los Angeles/ London.
Luiselli, M.M., 2011. Die Suche nach Gottesnähe. Untersuchungen zur Persönlichen Frömmigkeit in Ägypten von der Ersten Zwischenzeit bis zum Ende des Neuen Reiches, Ägypten und Altes Testament 73. Wiesbaden.
Nenna, M. and M. Seif-el Din, 2000. La vaisselle en faïnce d'epoque gréco-romaine. Catalogue du Museé gréco-romaine d'Alexandrie, Études alexandrines 4. Cairo.
Nicholson, P., 1993. Egyptian Faience and Glass. Dyfed.
Pinch, G., 1993. Votive Offerings to Hathor. Oxford.
Schott, S., 1952. Das schöne Fest vom Wüstentale. Festbräuche einer Totenstadt. Wiesbaden.
Seiler, A., 2005. Tradition & Wandel. Die Keramik als Spiegel der Kulturentwicklung Thebens in der Zweiten Zwischenzeit. Mainz.
Smith, M., 2009. Traversing Eternity. Texts for the Afterlife from Ptolemaic and Roman Egypt. Oxford.
Turner, V., 2008. The Ritual Process. Structure and anti-Structure. New Jersey.
Winlock, H.E., 1923. 'The Museum's Excavations at Thebes' in BMMA 18, December II, 11-39.
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text:
\section{Introduction}

Consider a high-energy coherent nuclear production process
\[
	a+A\rightarrow a^{\star}+A
\]
with quantum numbers exchanged those of the photon. Such a reaction
can be initiated by a one-photon
exhange, Coulomb production, or by strong interactions. The characteristic
feature of Coulomb production is a very sharp peak near the forward direction.
As energy increases the peak becomes sharper and at the same time moves
towards smaller angles. As a consequence, it becomes possible to disentangle Coulomb
and strong production. If the final state hadron $a^{\star}$
is a resonance  the decay rate $\Gamma (a^{\star}\rightarrow a\gamma)$
can be determined. This was first noticed by
Primakoff \cite{1}, and many radiative decay rates have been determined this way.
 A unified theoretical description of both strong and Coulomb production
within the Glauber model was presented in  ref.~\cite{2}.

The final state hadron $a^{\star}$ need not be a resonance. It can
also be a multiparticle state. In that case Coulomb production gives information
on the cross section for the reaction
$ \gamma + a \rightarrow \gamma +a^{\star}$ \cite{3}. An example is pionic Coulomb
production or bremsstrahlung,
\[
\pi^- +A\rightarrow\pi^- +\gamma +A
\]
which is driven by low-energy Compton scattering $\gamma+\pi^- \rightarrow \gamma+\pi^-$.
It has been suggested \cite{4}, that by studying pionic Coulomb
production  important information on the
Compton amplitude can be extracted. The low-energy Compton scattering amplitude
is a sum of two contributions,  a structure-independent
Thomson term, and a  structure-dependent Rayleigh term. The latter is fixed by the pion
polarisability, and could, under ideal circumstancies be determined
in high-energy nuclear Coulomb production.
 An experiment with this aim
 has been performed  \cite{5}, and a reasonable value for the pion
 polarisability was extracted.

We shall investigate pionic Coulomb production within the Glauber model
\cite{6}. In particular, we are interested in determining the nuclear
form factors that accompany the various terms in the underlying
Compton amplitude.

Our presentation is arranged as follows. First, we recall the
theoretical description of low-energy pion Compton scattering.
Then, we use this information to develop, in the Born approximation,
the nuclear small-angle amplitude for pionic Coulomb production.
Finally, we show how these expressions are changed when
nuclear multiple scattering is taken into account. Coulomb as well
as nuclear multiple scattering is considered.

\newpage
\section{Pion Compton scattering}

The driving amplitude for pionic Coulomb production is the the low-energy
pion Compton amplitude. It is important to understand the origin and structure
of the various contributions to this amplitude since different sub amplitudes
might lead to different form factors when embedded in the nucleus. That
we need the low-energy amplitude can be understood by looking at the the
reaction from a coordinate system where the initial pion is at rest and the
nucleus runs past at high speed. Since we are in the Coulomb region
the momentum transfer is extremely tiny and the kick to the pion
consequently very gentle.

The Compton amplitude can be written as
\[
{\mathcal M}(\gamma(q_1)\pi^-(p_1)\rightarrow \gamma(q_2)\pi^-(p_2))=
  {\mathcal M}_{\mu\nu}\epsilon_1^{\mu}(q_1)\epsilon_2^{\nu}(q_2)\ .
\]
Gauge invariance requires that, for real as well as virtual photons
with  $q^2\neq0$, the Compton tensor satisfies
\[
  {\mathcal M}_{\mu\nu}q_1^{\mu}= {\mathcal M}_{\mu\nu}q_2^{\nu}=0 \ .
\]
We need the dominant contributions to the amplitude at small c.m.
energies. They are the Born terms and the polarisability terms.

For pions there are three Born amplitudes described by the
Feynman diagrams of fig.~1.
\begin{figure}[ht]
\begin{tabular}{c@{}c@{}c@{}}
\scalebox{1.0}{\includegraphics{cpt1.eps}}&\quad
\scalebox{1.0}{\includegraphics{cpt2.eps}}&\quad
\scalebox{1.0}{\includegraphics{cpt3.eps}}
 \end{tabular}
 \caption{Born diagrams for pion Compton scattering.}
  \label{fig:1}
\end{figure}\\
\noindent
Their sum is gauge invariant
\begin{equation}
  {\mathcal M}_{\mu\nu}^{B}= ie^2\left[ 2g_{\mu\nu}
  -\frac{(2p_2+q_2)_{\nu}(2p_1+q_1)_{\mu}}{2p_2\cdot q_2}
  -\frac{(2p_1-q_2)_{\nu}(2p_2-q_1)_{\mu}}{-2p_1\cdot q_2}\right].
\label{Compton_Born}
\end{equation}
This expression is correct also when $q_1^2\neq 0$, and
that will be important for our applications.
In the low-energy limit  the amplitude $ {\mathcal M}_{\mu\nu}^{B}$
 reduces to the structure-independent Thompson term.

Terms quadratic in the photon energies are structure dependent,
Rayleigh terms.  They come from diagrams like
\begin{figure}[ht]
\begin{tabular}{c@{}c@{}c@{}}
\scalebox{1.10}{\includegraphics{ray1.eps}}&\quad
\scalebox{1.10}{\includegraphics{ray3.eps}} &\quad
 \scalebox{1.10}{\includegraphics{ray4.eps} }
 \end{tabular}
  \caption{One-loop Feynman diagrams in chiral-Lagrangian theory.}
\end{figure}\\
\noindent
In second order of the photon momenta we can construct
two gauge invariant Compton tensors, which we choose to be
\begin{equation}
 {\mathcal M}_{\mu\nu}^{I}= ie^2\,
        \displaystyle{       \frac{2m_{\pi} \beta_{\pi}}{\alpha} }
   \bigg[ q_1\cdot q_2\, g_{\mu\nu} -q_{2\mu} q_{1\nu} \bigg]
\label{Compton_pol_I}
\end{equation}
with $\beta_{\pi}$ the magnetic polarisability, and
\begin{equation}
\begin{array}{rl}
 {\mathcal M}_{\mu\nu}^{II}=& ie^2  \,
   \displaystyle{ \frac{-2(\alpha_{\pi}+\beta_{\pi})}{m_{\pi}\alpha} }
   \bigg[ p_1\cdot q_1 p_1\cdot q_2\, g_{\mu\nu}
        +q_1\cdot q_2\, p_{1\mu}p_{1\nu} \\
 &  -p_1\cdot q_1 \, q_{2\mu}p_{1\nu}
   -p_1\cdot q_2\,  p_{1\mu}q_{1\nu} \bigg]
\end{array}
\label{Compton_pol_II}
\end{equation}
with $\alpha_{\pi}$ the electric polarisability.
The  Compton amplitude  is the sum of the above individual
contributions, expressions (\ref{Compton_Born}), (\ref{Compton_pol_I})
and (\ref{Compton_pol_II}).
Evaluated in the  lab system (initial pion at rest) the Compton
amplitude reads
\[
\begin{array}{rl}
 {\mathcal M}=& i8\pi m_{\pi} \big[
  \displaystyle{ -\frac{\alpha}{m_{\pi}}   }
  \bmath{\epsilon}_1\cdot  \bmath{\epsilon}_2 \\
& +  \alpha_{\pi}\omega_1\omega_2 \bmath{\epsilon}_1\cdot  \bmath{\epsilon}_2
  +\beta_{\pi}(\bmath{q}_1\times\bmath{\epsilon}_1)\cdot
       (\bmath{q}_2\times\bmath{\epsilon}_2)\big] \ .
\end{array}
\]

In ChPT one obtains in the one-loop order \cite{7}
\[
 \alpha_{\pi^\pm}=- \beta_{\pi^\pm}=2.7\cdot10^{-4} \ \mbox{\rm fm}^3.
\]
In this order one has,  $\alpha_{\pi^\pm}+ \beta_{\pi^\pm}=0$, and
we shall assume this relation throughout. Also two-loop contributions to
the polarisabilities have been calculated \cite{8}, and found to be small.
Therefore, we  put ${\mathcal M}_{\mu\nu}^{II}=0.$ It is useful to
introduce the dimensionless parameter
\begin{equation}
 \lambda=    \frac{\beta_{\pi^\pm}m_{\pi^\pm}^3 }{\alpha }
   = - 0.013 \ .
\label{lambda-def}
\end{equation}
There is no agreement on the experimental value of the polarisability
so we shall use the value (\ref{lambda-def}) as a guide in our deliberations.
\newpage
\section{Pionic bremsstrahlung: Born approximation}

Pionic bremsstrahlung can be accompanied both by electromagnetic
and strong interactions. We are interested in the region
of small momentum transfers to the nucleus, and in particular the Coulomb region.
This means that when the pion interaction with the nucleus is
through a one-photon exchange, then the relevant Compton
amplitude is a low-energy amplitude, as desired.

The kinematics of pionic bremsstrahlung  is
\[
\pi^-(p_1) +A(p)\rightarrow\pi^-(p_2) +\gamma(q_2) +A(p') \ .
\]
Our interest is focussed on coherent high-energy interactions
where the energies of the pions, as well as that of the radiated
photon, are many GeV:s. Coherence demands that the transverse
momenta $\bmath{p}_{2\bot}$ and $\bmath{q}_{2\bot}$
be much smaller than the inverse of the nuclear radius $R_A$,
and as a consequence of the high energies, the longitudinal momentum transfer to
the nucleus may be ignored. Thus, to a precision sufficient for the
subsequent analysis
we put
\[
p_{1z} = p_{2z} +q_{2z}
\]
with $z$ denoting the longitudinal direction. The energy transfer
to the nucleus can likewise be ignored.

The one-photon exchange graph is pictured in fig.~3. The small blob in the
\begin{figure}[h]\begin{center}
\scalebox{1.20}{\includegraphics{nucpt.eps}}
\end{center}
\caption{Born diagram for pionic bremsstrahlung.}
\end{figure}
graph represents the full
pion-Compton amplitude;
the large blob the photon-nucleus electromagnetic vertex.
The pion charge is $-e$, the nuclear charge $Ze$, and
the nucleus is treated as a spin-zero particle.
With $q_1$ the virtual photon four-momentum, these
assumptions lead to a
Coulomb production amplitude
\begin{equation}
  {\mathcal M}_{C}=\frac{-i}{q_1^2}
   {\mathcal M}_{\mu\nu}(p_2,q_2;p_1,q_1)(-iZe)
             (p+p')^{\mu}\epsilon_2^{\nu} \ .
\label{Coulomb_Born}
\end{equation}
Since the Compton tensor $ {\mathcal M}_{\mu\nu}$ is
 gauge invariant we may also make the
replacement $p+p'=2p+q_1\rightarrow 2p$.

The expression for  ${\mathcal M}_{C}$  is covariant and valid
in all coordinate systems. We prefer to work in the lab system where the
initial nucleus, of mass $M_A$, is at rest. Choosing a polarisation
vector $\epsilon_2$ with
vanishing time  component, leads to
\begin{equation}
 \begin{array}{rcl}
  {\mathcal M}_C & =&  8i\pi M_A\, \displaystyle{ \frac{-2Z\alpha}{q_1^2} }\,e
  \bigg[
  \left( \frac{E_1\bmath{p}_2\cdot \bmath{\epsilon}_2}{p_2\cdot q_2}
 -\frac{E_2\bmath{p}_1\cdot \bmath{\epsilon}_2}{p_1\cdot q_2}\right)
  \\ && \\ && \qquad  \qquad\qquad \qquad \qquad
   + \displaystyle{\frac{\lambda \omega_2}{ m_{\pi}^2} }\,
      (\bmath{p}_2-\bmath{p}_1)\cdot \bmath{\epsilon}_2
   \bigg] \ .
\end{array}\label{Coulomb_Born_lab}
\end{equation}

Here, the first two terms  originate from the Compton Born
terms of eq.(\ref{Compton_Born}).
The $g_{\mu\nu}$ Born term does not  contribute to $ {\mathcal M}_C$.
Instead, the first term  of (\ref{Coulomb_Born_lab}) originates from the middle term
of eq.(\ref{Compton_Born}) and represents a pion-nucleus elastic  scattering step
followed by a pionic bremsstrahlung step. Similarly,
 the second term of (\ref{Coulomb_Born_lab})
originates from the last term of eq.(\ref{Compton_Born}) and represents a
pionic bremsstrahlung step followed by a pion-nucleus elastic scattering step.

The last term of (\ref{Coulomb_Born_lab}), finally, is generated by the polarisability contribution,
eq.(\ref{Compton_pol_I}), to the Compton amplitude. In this term the
radiated and exchanged photons are attached to the same vertex.
The second polarisability contribution, eq.(\ref{Compton_pol_II}),
vanishes since we presume $\alpha_{\pi}+\beta_{\pi}=0$.

Pionic bremsstrahlung from the external pion legs can also occur
in nuclear interactions, as depicted in fig.~4.
For $\pi^-$ scattering,  with  $q_1=p-p'$
\begin{figure}[ht]\begin{center}
\begin{tabular}{c@{}c@{}}
\scalebox{1.40}{\includegraphics{pir2.eps}}&\qquad
\scalebox{1.40}{\includegraphics{pir1.eps}}
 \end{tabular}\end{center}
 \caption{Pion bremsstrahlung in nuclear scattering.}
\end{figure}
the four-momentum transfer to the nucleus, as above, the nuclear
contribution to pionic bremsstrahlung reads
\begin{equation}
  {\mathcal M}_N = e\bigg[  - \frac{\epsilon_2\cdot p_2}{p_2\cdot q_2}
   {\mathcal M}_{\pi A}(s_1,q_1)
  +  \frac{\epsilon_2\cdot p_1}{p_1\cdot q_2}
    {\mathcal M}_{\pi A}(s_2,q_1)
    \bigg] \ .
\label{Brems-init}
 \end{equation}
Here, ${\mathcal M}_{\pi A}(s,q)$ is the elastic pion-nucleus scattering amplitude
at energy $s$ and momentum transfer $q$. The nuclear scattering steps occur with the same
momentum transfer. In the first term of (\ref{Brems-init}) the
pion-nucleus scattering occurs after the photon is radiated, and the
amplitude should  therefore be evaluated at energy $s_2=(p_2+p')^2$.
Similarly,  the pion-nucleus amplitude of the second term of eq.(\ref{Brems-init})
is evaluated at $s_1=(p_1+p)^2$.
To insure gauge invariance of ${\mathcal M}_N$ one could, {\it e.g.},
evaluate the  pion-nucleus amplitudes at
the same energy $s$. The alternative is to add an appropriate
counter term arising from internal radiation. We shall not do so, however,
but shall take the amplitude (\ref{Brems-init}) as it stands. The error
committed is probably negligible.

The pion-nucleus amplitude $ {\mathcal M}_{\pi A}(s,q)$
is related to the pion-nucleus elastic scattering amplitude in the
lab system, $F_N(E,\bmath{q})$, through
\begin{equation}
   {\mathcal M}_{\pi A}(s,q)=8i\pi M_A \, F_N(E,\bmath{q})
\label{M-lab_amp}
 \end{equation}
 with $E$ the pion lab energy. The  amplitude $F_N(E,\bmath{q})$
 depends only on the transverse part $\bmath{q}_\bot$ of $\bmath{q}$.

In our application we are in an energy region where the pion-nucleus
total cross section $\sigma_{\pi A}$ may be considered independent of energy.
If in addition, we specialise to the region of
Coulomb production the dependence on momentum transfer can
be ignored, and  a simple energy dependence emerges
\begin{equation}
   F_N(E,0)=\frac{ik}{4\pi}\sigma_{\pi A}(1-i\alpha_{\pi A})
 \equiv\frac{ik}{4\pi}\sigma_{\pi A}' \ .
 \end{equation}
Since at high energies there is no
distinction between $k$ and $E$
we can write the nuclear bremsstrahlung contribution as
\begin{equation}
  {\mathcal M}_N =8i\pi M_A \,\frac{i e\sigma_{\pi A}'}{4\pi}
  \bigg[
  \frac{E_1 \bmath{\epsilon}_2\cdot \bmath{p}_2}{p_2\cdot q_2}
   - \frac{E_2\bmath{\epsilon}_2\cdot \bmath{p}_1}{p_1\cdot q_2}
    \bigg]  \ .
\label{Nuclear_brems}
 \end{equation}
The factor inside the brackets is identical to the corresponding
 factor in eq.(\ref{Coulomb_Born_lab}) describing radiation
 from the external legs.

The strong  pion-nucleus amplitude $ {\mathcal M}_{\pi A}$
is conveniently calculated in the
Glauber model. Further details below.
\newpage
\section{Elastic Coulomb scattering}

At this point it is useful to recall the eikonal description
of elastic Coulomb scattering. The Coulomb potential
for $\pi^-$-nucleus scattering is
\begin{equation}
  V_C(\bmath{r})= -\frac{Z\alpha}{r}
\label{Coul_pot}
 \end{equation}
and the scattering amplitude in the Born approximation
\begin{equation}
  f_C(E,\mathbf{q})= -\frac{E}{2\pi}\int\textrm{d}^3x\,
   e^{-i\mathbf{q}\cdot\mathbf{x}}\,V_C(\mathbf{r})
   =\frac{2Z\alpha E}{\mathbf{q}^2}
\label{Rel_Born}
\end{equation}
with the momentum transfer $\bmath{q}=\bmath{k}'-\bmath{k}$.
In reality, at high energies the momentum tranfer is
transverse so that $\mathbf{q}=\mathbf{q}_\bot$.

Elastic Coulomb scattering to all orders in the fine-structure constant
is exactly reproduced by the eikonal approximation
\begin{equation}
  f_C(E,\mathbf{q})= \frac{ik}{2\pi }
    \int\textrm{d}^2b\, e^{-i\mathbf{q}\cdot\mathbf{b}}
   [1 - e^{i\chi_C(\mathbf{b})}]
\label{Rel_eik}
\end{equation}
with the point-like Coulomb phase function
\begin{eqnarray}
  \chi_C(\mathbf{b})&=& -\eta \ln (b/2a)
                       \label{Point-Coul-phase}\\
  \eta&=& 2Z\alpha/v \ .
\end{eqnarray}
Here, $a$ is a cut-off parameter introduced in order to
make the phase function finite. The Coulomb potential is
cut off at a radius $r=a$.

At high energies there is no distinction between $E$ and $k$, and
$v=1$. A straightforward integration gives the well-known result
\begin{eqnarray}
  f_C(E,\mathbf{q}) &=& \frac{2Z\alpha E}{\mathbf{q}^2}
   \exp [i\sigma_{\eta} + i\eta \ln (aq)] \label{Point-cross}\\
    \sigma_{\eta} &=& 2\arg\Gamma(1-i\eta/2) \ .
\end{eqnarray}

A thorough description of Coulomb scattering in the eikonal
approximation can be found in
\cite{6}, but also \cite{9} contains useful information. For an extended
charge distribution the phase-shift function takes the form
\begin{equation}
	\chi_C(b)=-\eta \left[\ln(b/2a)
	    + 2\pi \int_b^{\infty}T(b')\ln(b'/b)b'\textrm{d} b'\right]
	     \label{Coul-ext-ch}
\end{equation}
where the target-thickness function $T(b)$ corresponds to a
nuclear charge-density distribution
normalised to unity.

In the real world pions obey the Klein-Gordon equation which contains
one term that is linear in the Coulomb potential $V_C(\bmath{r})$,
and one which is quadratic. The above applies to the linear term.
The quadratic term leads to corrections that can be expanded
in powers of $\sin\theta/2=q/2k$. For a point charge in the Klein-Gordon
case \cite{10}
\begin{eqnarray}
	f_C^{KG}(E,\mathbf{q})&=&f_C(E,\mathbf{q})
	 \left\{ 1+\frac{\pi(Z\alpha)^2e^{i\sigma_1}}{\eta}\frac{q}{2k} + \ldots \right\}\\
	 \sigma_1&=& 2 [\arg \Gamma(\half+i\eta/2) -\arg \Gamma(1+i\eta/2) ] \ .
\end{eqnarray}
A few of the higher order corrections have also been evaluated \cite{11}.
The important point for us is that we consider the very small
angular region where the correction terms safely can be  neglected.
The corrections due to the extension of the nuclear charge
distribution are negligible as well.

\newpage
\section{Pionic bremsstrahlung: eikonal approximation}

The Born amplitudes are strongly modified by nuclear multiple
scattering, a modification most easily calculated in the
eikonal approximation. But first a  remark on the four-momentum
transfer to the nucleus, $q_1$. Its time component can always be
neglected, so that
\begin{equation}
 - q_1^2=  \mathbf{q}_1^2 = \mathbf{q}_{1\bot}^2+q_{1z}^2 \ .
\end{equation}
The longitudinal momentum transfer $-q_{1z}$ is tiny and can
be replaced by its minimum value
\begin{equation}
	q_{min}
	  =\frac{m^2\omega_2}{2E_1E_2} \label{min-mom}
\end{equation}
but we shall start by neglecting $q_{1z}$ altogether and later return to
the modifications dictated by its  presence.

In the Coulomb-induced bremsstrahlung amplitude (\ref{Coulomb_Born_lab}),
 Coulomb scattering in the one-photon approximation is
described by the factor
\begin{equation}
\frac{2Z\alpha E_1}{\mathbf{q}_{1\bot}^2} \ .\label{new-Born}
\end{equation}
The very first term of (\ref{Coulomb_Born_lab}) represents
Coulomb scattering followed by  brems\-strahlung. To include multiple
Coulomb scattering we add all diagrams with multiple-photon exchanges
between the pion and the nucleus. If all these exchanges
occur before the bremsstrahlung step then we simply
replace the Born amplitude (\ref{new-Born}) by the full
Coulomb amplitude of eq.(\ref{Rel_eik}). The contributions
from the diagrams where radiation occurs from an intermediate
pion line, {\it i.e.}, when we have photon exchanges both before and
after the radiation step, cancel to a large extent. Therefore,
diagrams with radiation from internal lines are ignored. The
corresponding argument applies to the second term of
(\ref{Coulomb_Born_lab}) as well.

The nuclear-induced bremsstrahlung amplitude (\ref{Brems-init}),
must be similarly modified.
The pion can radiate when between two nucleon
collisions, if we view the nuclear interaction as caused by
multiple interactions between the pion and the nucleons
of the nucleus. Again, the contributions from the internal
radiation diagrams cancel when summed.

A further generalisation is to include Coulomb and nuclear exchanges
simultaneously. Since internal radiation
diagrams are ignored we get
\begin{equation}
  {\mathcal M}_{rad}= 8\pi iM_A e  \bigg[ -
  \displaystyle{ \frac{E_2\bmath{p}_1\cdot \bmath{\epsilon}_2}{p_1\cdot q_2} }
     +
  \displaystyle{ \frac{E_1\bmath{p}_2\cdot \bmath{\epsilon}_2}{p_2\cdot q_2}}
    \bigg]{\mathcal F}_{rad}(\bmath{q}_{1\bot}) \ . \label{Ext-Ka}
\end{equation}

The factor $ {\mathcal F}_{rad}(\bmath{q}_\bot)$ is
the pion-nucleus
scattering amplitude, including both its Coulomb and nuclear
interactions. In the Glauber model
\begin{equation}
  {\mathcal F}_{rad}(\bmath{q}_\bot)=
  \frac{iv}{2\pi }
    \int\textrm{d}^2b\, e^{-i\mathbf{q}_\bot\cdot\mathbf{b}}
   \left( 1 - e^{i(\chi_C(\mathbf{b})+\chi_N(\mathbf{b}))}\right)
 \label{FGl_C+N}
\end{equation}
with the momentum transfer $\mathbf{q}_\bot$ in the impact parameter plane.
The function
${\mathcal F}_{rad}(\bmath{q}_\bot)$ is energy independent, providing
we can put $v=1$ and neglect the  energy dependence of the pion-nucleus
potentials. The phase-shift functions are related to
the corresponding potentials, whether Coulomb or nuclear,
through
\begin{equation}
  \chi(\mathbf{b})=
  \frac{-1}{v }
    \int_{-\infty}^{\infty}\textrm{d} z\,V(\mathbf{b},z) \ .
 \label{Def-phase-fcn}
\end{equation}

We can, in a well-known fashion, decompose ${\mathcal F}_{rad}(\bmath{q})$
into a purely
Coulomb and a Coulomb-distorted nuclear amplitude by writing
\begin{eqnarray}
	{\mathcal F}_{rad}(\bmath{q}_\bot)&=&
	    \frac{iv}{2\pi }
    \int\textrm{d}^2b\, e^{-i\mathbf{q}_\bot\cdot\mathbf{b}}
   \left( 1 - e^{i\chi_C(\mathbf{b})}\right)\nonumber \\
      &&+
  \frac{iv}{2\pi }
    \int\textrm{d}^2b\, e^{-i\mathbf{q}_\bot\cdot\mathbf{b}}e^{i\chi_C(\mathbf{b})}
   \left( 1 - e^{i\chi_N(\mathbf{b})}\right)\nonumber\\
     &\equiv & [f_C(E, \bmath{q}_\bot)+f_{N}(E, \bmath{q}_\bot)]/E \ .
 \label{Decomp-C+N}
\end{eqnarray}
The analytic expression of the Coulomb  amplitude
  $f_C(E, \bmath{q}_\bot)$ for a point charge distribution
  is  given in eq.(\ref{Point-cross}).

The polarisation-induced bremsstrahlung amplitude is the third
term of (\ref{Coulomb_Born_lab}).  Before proceeding we note  the identities
$(\bmath{p}_2-\bmath{p}_1)\cdot \bmath{\epsilon}_2=
\bmath{q}_1\cdot \bmath{\epsilon}_2$ and
\begin{equation}
  \displaystyle{ \frac{2Z\alpha}{\bmath{q}_1^2} } \,
        \bmath{q}_1\cdot \bmath{\epsilon}_2
  =  \displaystyle{\frac{i}{2\pi}} \int\textrm{d}^3r\,
   e^{-i\mathbf{q}_1\cdot\mathbf{r}}\, \bmath{\epsilon}_2\cdot \bmath{\nabla}
   V_C(\bmath{r}) \ .\label{simp-pol}
\end{equation}
The polarisation potential is hence proportional to the gradient of
the Coulomb potential. We now replace the plane waves of the Born approximation
by distorted waves,
 assume energy-independent  pion-nucleus
potentials and neglect  the longitudinal momentum transfer $q_{1z}$.
  Introducing phase-shift functions instead of
potentials leads to the energy-independent expression,
  $v=v_1=v_2$,
\begin{equation}
  \displaystyle{\frac{-i v}{2\pi}} \int\textrm{d}^2b\,
   e^{-i\mathbf{q}_{1\bot}\cdot\mathbf{b}}\,
   \bmath{\epsilon}_2\cdot \bmath{\nabla} \chi_C(\mathbf{b})
  e^{ i(\chi_C(\mathbf{b})+\chi_N(\mathbf{b})) } \ .
  \label{Eik_pol-factor}
\end{equation}
With help of the identity
\begin{equation}
  e^{ i(\chi_C(\mathbf{b})+\chi_N(\mathbf{b})) }=
   e^{ i\chi_C(\mathbf{b})} - e^{ i\chi_C(\mathbf{b})}
   (1-e^{ i\chi_N(\mathbf{b})})\label{subdiv}
\end{equation}
we can easily isolate a purely Coulombic term from a rest term
which involves also nuclear effects.
After  partial integration of the first term of (\ref{subdiv})
and an angular integration of the second one, expression
(\ref{Eik_pol-factor}) can be written as
\begin{equation}
	\mathbf{q}_{1\bot}\cdot\bmath{\epsilon}_2{\mathcal F}_{pol}(\bmath{q}_{1\bot}) \ .
\end{equation}
The energy-independent form factor ${\mathcal F}_{pol}(\bmath{q}_{1\bot})$ is
\begin{equation}
	{\mathcal F}_{pol}(\bmath{q}_{\bot})=
	[f_C(E,\mathbf{q}_\bot) + f_{P}(E,\mathbf{q}_\bot) ]/E
\end{equation}
with $f_C(E,\mathbf{q}_\bot)$ the elastic Coulomb scattering amplitude
and the new amplitude $f_{P}(E,\mathbf{q}_\bot)$
 defined by, $q_\bot=\| \mathbf{q}_\bot\|$,
\begin{equation}
	f_{P}(E,\mathbf{q}_\bot)=k\int_0^{\infty}b^2\textrm{d} b\, \frac{J_1(q_\bot b)}{q_\bot b}
	  \frac{\textrm{d} \chi_C(b)}{\textrm{d} b}e^{ i\chi_C(b)}(1-
  e^{i \chi_N(b)}) \ .\label{f-pol-fcn}
\end{equation}
The last factor of the integrand guarantees that the integrand
vanishes outside
the nuclear mass distribution.
From the definition of the Coulomb phase for extended
charge distributions, eq.(\ref{Coul-ext-ch}), we derive
\begin{equation}
  \frac{\textrm{d} \chi_C(b)}{\textrm{d}  b}= -2\pi\eta \frac{1}{b}
   \int_0^b b'\textrm{d} b'\, T(b') \ .
\end{equation}

The result of all this is a polarisation contribution to the bremsstrahlung amplitude
\begin{equation}
  {\mathcal M}_{pol}=  8\pi i e M_A \bigg[ \frac{ \lambda}{m_{\pi}^2}   \, \omega_2
   \mathbf{q}_1\cdot \bmath{\epsilon}_2
    \bigg]{\mathcal F}_{pol}(\bmath{q}_{1\bot})\ .\label{Pol-Ka}
\end{equation}
To get  the complete  ${\mathcal M}$-amplitude we add the amplitude
${\mathcal M}_{rad}$ representing radiation from external legs;
\begin{eqnarray}
  {\mathcal M}&= & 8\pi i e M_A \bigg\{ \big[ -
  \displaystyle{ \frac{E_2\bmath{p}_1\cdot \bmath{\epsilon}_2}{p_1\cdot q_2} }
     +
  \displaystyle{ \frac{E_1\bmath{p}_2\cdot \bmath{\epsilon}_2}{p_2\cdot q_2}}
    \big]{\mathcal F}_{rad}(\bmath{q}_{1\bot}) \nonumber \\
   && \quad \quad +
  \big[ \frac{ \lambda}{m_{\pi}^2}   \, \omega_2
   \mathbf{q}_1\cdot \bmath{\epsilon}_2
    \big]{\mathcal F}_{pol}(\bmath{q}_{1\bot}) \bigg\}\ . \label{Full-M-amp}
\end{eqnarray}

So far we have kept the cut-off parameter $a$ of the Coulomb potential. This
was intentional. We now remove the dependence on this parameter by
removing a phase factor common to all amplitudes. This is
conventionally done so that the Coulomb phase in the integrand of the
nuclear amplitude,
$f_{N}(E,\bmath{q}_\bot)$ eq.(\ref{Decomp-C+N}), varies as slowly as possibly
over the domain of integration. Since the main
contribution  comes from a region close to the nuclear rim,
this goal is achieved by setting $2a=R_u$ in eq.(\ref{Coul-ext-ch}). Here, $R_u$
is the equivalent radius of the uniform nuclear mass distribution.

Let us now return to the question of the longitudinal momentum
transfer, $q_{min}$. In the nuclear and polarisation amplitudes,
eqs (\ref{Decomp-C+N}) and (\ref{f-pol-fcn}), the integration is
over the nuclear region, which has a finite extension. Since
$q_{min}R_u\ll 1$ all dependence on $q_{min}$ can be ignored.
Extracting  appropriate phase factors we may write,
with $q_\bot=\|\mathbf{q}_\bot\|$,
\begin{eqnarray}
	f_{N}(E,\mathbf{q}_\bot) &= &
     ik e^{i\delta_B} \int b\textrm{d} b\, J_0(q_\bot b)
   \left( 1 - e^{i\chi_N(b)}\right)
 \label{fCN-new} \\
 f_{P}(E,\mathbf{q}_\bot)& =&
	    k e^{i\delta_{B}'}
    \int_0^{\infty}b^2\textrm{d} b\, \frac{J_1(q_\bot b)}{q_\bot b}
	  \frac{\textrm{d} \chi_C(b)}{\textrm{d} b}
	  (1-e^{i \chi_N(b)})
 \label{fCP-new}
\end{eqnarray}
for the nuclear and polarisation amplitudes. The Bethe phases $\delta_B$
and $\delta_{B}'$ need not be factorised as indicated. The original
integrations could also have been carried out.

The pure Coulomb amplitude is more of a problem. In the Born approximation,
as layed out in eq.(\ref{Coulomb_Born}), the Coulomb denominator
contains the longitudinal momentum transfer through
$ \mathbf{q}_1^2 = \mathbf{q}_{1\bot}^2+q_{min}^2 $. When $q_\bot\gg q_{min}$
the dependence on $q_{min}$ can safely be ignored, but under the Coulomb peak,
where $q_\bot\approx q_{min}$ that is not possible. A subsequent question
is then how the nuclear form factor depends on $q_{min}$. This
question has not yet been resolved analytically. Of course, the scattering
amplitude can be calculated numerically, but until we have done so we
suggest the point-charge Coulomb amplitude be chosen as
\begin{equation}
  f_C(E,\mathbf{q}_\bot) = \frac{2Z\alpha E}{\mathbf{q}_\bot^2 +q_{min}^2}\,
   \exp [i\sigma_{\eta} + i\eta \ln (q_\bot R_u/2)] \ .\label{Point-cross-final}
\end{equation}
The form factor for extended charge distributions can,
as is necessary for large momentum transfers, be calculated as in ref.\cite{9}.
\newpage
\section{Cross sections}

The cross section distribution in the lab system is
\begin{equation}
	\textrm{d} \sigma =\frac{1}{4p_1 M_A} \left| {\mathcal M}\right|^2 {\rm dLips}
\end{equation}
where $p_1$ is the incident pion lab momentum. The Lorentz-invariant phase space
is as always
\begin{eqnarray}
{\rm dLips} &=& (2\pi)^4 \delta(p_1+p_A-p_2-q_2-p_A')
  \frac{\textrm{d}^3p_A'}{ (2\pi)^3 2E_A'}  \frac{\textrm{d}^3p_2}{ (2\pi)^3 2E_2 }
  \frac{\textrm{d}^3q_2}{ (2\pi)^3 2\omega_2} \nonumber \\
  &=& \frac{1}{16\pi M_A} \frac{\textrm{d}^2 p_{2\bot}}{(2\pi)^2}
    \frac{\textrm{d}^2q_{2\bot}}{(2\pi)^2}\frac{\textrm{d} q_{2z}}{p_{2z} q_{2z}} \ .
 \label{Phase-space}
\end{eqnarray}
The pion propagators of eq.(\ref{Full-M-amp}) can be rewritten as
\begin{eqnarray}
p_1\cdot q_2&=&
  \frac{1}{2x} \left[ \mathbf{q}_{2\bot}^2 + x^2 m_{\pi}^2 \right]\label{Propagator1}\\
 p_2\cdot q_2&=&
  \frac{1}{2x'} \left[ (\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})^2+ x'^2 m_{\pi}^2 \right]
 \label{Propagator2}
\end{eqnarray}
with the parameters
\begin{eqnarray}
x&=&
  \frac{q_{2z}}{p_1} =\frac{\omega_2}{E_1}\label{x-fraction}\\
 x'&=&\frac{q_{2z}}{p_{2z}} =\frac{\omega_2}{E_2}=\frac{x}{1-x} \ .
 \label{xprim-fraction}
\end{eqnarray}

The matrix element in eq.(\ref{Full-M-amp}) can be further
simplified. Since the polarisation vector $\bmath{\epsilon}_2$ lies in the plane
orthogonal to $\bmath{q}_2$,  the scalar products with the polarisation vector
can be  replaced by
 \begin{eqnarray}
\bmath{p}_1\cdot \bmath{\epsilon}_2&=&-\frac{1}{x}\,\bmath{q}_{2\bot}\cdot \bmath{\epsilon}_2 \\
\bmath{p}_2\cdot \bmath{\epsilon}_2&=&(\bmath{p}_{2\bot}-\frac{1}{x'}\,\bmath{q}_{2\bot}) \cdot \bmath{\epsilon}_2 \\
 (\bmath{p}_2 - \bmath{p}_1)\cdot \bmath{\epsilon}_2&=&\bmath{q}_{1\bot} \cdot \bmath{\epsilon}_2 \ ,
 \label{eps_products}
\end{eqnarray}
where perpendicular still means perpendicular to the incident pion direction. The new
expression for the matrix element becomes more transparent
\begin{eqnarray}
{\cal M}&=&16\pi ie M_A  \left[  \bigg\{
	 \frac{E_2\mathbf{q}_{2\bot}}{\mathbf{q}_{2\bot}^2 + x^2 m_{\pi}^2 }
	   - \frac{E_1(\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})}
	   { (\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})^2+ x'^2 m_{\pi}^2 }\bigg\}
	      {\mathcal F}_{rad}(\bmath{q}_{1\bot})\right.\nonumber \\
	    &&\left. \quad \quad+\frac{\lambda}{2}\frac{\omega_2\mathbf{q}_{1\bot}}{m_{\pi}^2}\,
	      {\mathcal F}_{pol}(\bmath{q}_{1\bot})\right]\cdot\bmath{\epsilon}_2
	 \label{Simple-amp}
\end{eqnarray}
and the summation over the photon polarisation directions embarrasingly trivial
\begin{eqnarray}
	\sum \left| {\cal M}\right|^2&=&64 (2\pi)^2 e^2 M_A^2
	 \nonumber \\
	 &&\times \left| \left[ \frac{E_2\mathbf{q}_{2\bot}}{\mathbf{q}_{2\bot}^2 + x^2 m_{\pi}^2 }
	   - \frac{E_1(\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})}
	   { (\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})^2+ x'^2 m_{\pi}^2 }\right]\right.
	      {\mathcal F}_{rad}(\bmath{q}_{1\bot})\nonumber \\
	    &&\left. \quad \quad+\frac{\lambda}{2}\frac{\omega_2\mathbf{q}_{1\bot}}{m_{\pi}^2}\,
	      {\mathcal F}_{pol}(\bmath{q}_{1\bot})\right|^2
	 \label{Amp-squared}
\end{eqnarray}

We recall that $\bmath{q}_1$ is the momenum transfer to the nucleus and
 \begin{equation}
	\bmath{q}_{1}=\bmath{q}_{2}+\bmath{p}_{2}
\end{equation}
with $\bmath{p}_{2}$ the momentum of the final state pion and $\bmath{q}_{2}$
the momentum of the final state photon. In eq.(\ref{Amp-squared})
only the dependence on $\bmath{q}_{1\bot}$ is indicated. The longitudinal
component is fixed by the relation
\begin{equation}
	- q_{1z}=\frac{1}{2p_1}[2p_2\cdot q_2+\bmath{q}_{1\bot}^2] \ .
	 \label{Min-mom-tr}
\end{equation}
For all practical purposes it can be replaced by its value in the forward
direction, $-q_{1z}=q_{min}$, with $q_{min}$ as given by eq.(\ref{min-mom}).
As a consequence, the denominator $\bmath{q}_1^2=\bmath{q}_{1\bot}^2+ q_{1z}^2$
of the Coulomb amplitude
 never vanishes. However, the factor
multiplying the form factor ${\mathcal F}_{rad}$ in eq.(\ref{Amp-squared})
vanishes in the forward direction, since there
 $\bmath{p}_1\cdot \bmath{\epsilon}_2 =\bmath{p}_2\cdot \bmath{\epsilon}_2=0$.

The cross section distribution  is dominated by the
first term of eq.(\ref{Amp-squared}) which is multiplied by the
form factor ${\mathcal F}_{rad}$. The second term is proportional to
the polarisability parameter $\lambda$ and the form factor  ${\mathcal F}_{pol}$
and is generally smaller. Since
${\mathcal F}_{rad}$ is exactly the amplitude we encounter in elastic
pion-nucleus scattering, this observation allows us to
distinguish three regions, characterised by increasing values
of the momentum transfer:
\begin{enumerate}
	\item {dominance of Coulomb bremsstrahlung}
	 	\item {competition between Coulomb and nuclear bremsstrahlung}
	 		\item {dominance of nuclear bremsstrahlung}
\end{enumerate}

In order to localise the proper Coulomb region we first localise
the overlap region where Coulomb and nuclear contributions are
of similar size. That happens when in the form factor ${\cal F}_{rad}$,
eq.(\ref{Decomp-C+N}), the Coulomb $f_C$ and  nuclear $f_N$ amplitudes
are equal in size. This, according to eq.(\ref{Forw-nucl-value}), is
roughly the case when
\begin{equation}
	\frac{2Z\alpha}{\bmath{q}_{1\bot}^2}=\frac{1}{2}R_u^2 \ .
\end{equation}
Putting $Z=A/2$ as a further approximation gives
\begin{equation}
	\bmath{q}_{1\bot}^2\approx\frac{2\alpha}{r_0^2}A^{1/3}=
	0.5\cdot10^{-3}A^{1/3}\quad {\rm (GeV/c)}^2 \ .
\end{equation}
Consequently, in the transition region we have for a typical nucleus
$|t|\approx10^{-3}$ (GeV/c)$^2$; in the Coulomb-dominated region
$|t|\approx10^{-4}$ (GeV/c)$^2$; and in the nuclear-dominated region
$|t|\approx10^{-2}$ (GeV/c)$^2$.

In the form factor ${\mathcal F}_{pol}$ the nuclear contribution
$f_{P}$ is substantially smaller than the corresponding $f_{N}$ in
${\mathcal F}_{rad}$ and would thus need larger momentum transfers
to make itself noticed.
For Cu the ratio $|f_P(E,0)/f_N(E,0)|=0.12$ derived from the formulae
in the Appendix, supports this statement.

There are  kinematic variables, beside those chosen above,
 that are of fundamental interest, {\it e.g.},
\begin{eqnarray}
	t&=&q_1^2\\
	s&=&(p_2+q_2)^2\\
	\Delta&=& (p_2-p_1)^2
\end{eqnarray}
which relate to properties of the underlying pion-Compton scattering
process. In fact, $t$ is the squared momentum transfer to the nucleus, but also
the squared mass of the virtual photon; $s$ is the square of the c.m.~energy
  and $\Delta$ the squared
momentum transfer in the  pion-Compton  scattering process.
A simple calculation ends in the results
\begin{eqnarray}
	t&=&-\bmath{q}_{1\bot}^2-\left(\frac{\omega_2m_{\pi}}{2E_1E_2}\right)^2m_{\pi}^2 \\
	s&=&\frac{E_1}{E_2}m_{\pi}^2+\frac{1}{x'} (\mathbf{q}_{2\bot}-x' \mathbf{p}_{2\bot})^2\\
	\Delta&=& -\frac{E_1}{E_2}\left[\mathbf{p}_{2\bot}^2+x^2m_{\pi}^2\right] \ .
\end{eqnarray}
From the expression for $s$ we conclude that in the Coulomb region
the Compton scattering takes place at a lab energy of
\[
\omega_{lab}=\half x'm_{\pi}\ .
\]
Similarly, from the expression for $\Delta$ we conclude that the scattering angle
in the pion-Compton c.m.~system is $\theta_{cm}=90^\circ$, and in the lab system
\[
 \cos\theta_{lab} =-\frac{E_1-E_2}{E_1+E_2}=-\frac{x}{2-x}\ .
 \]
When $x'$ is large, which is an interesting region, then $\omega_{lab}$
 is also large, and one can legitimately ask where our basic
amplitude for the Compton process breaks down.

Finally, there is the question of region of applicability of the
model described above. It is commonly stated that the radiation
from the external legs
dominates as long as the propagator denominators,
eqs  (\ref{Propagator1}) and (\ref{Propagator2}),   are of order
$m_{\pi}^2$ or smaller. Our formulae should therefore work
well into the nuclear region. A quantification
of this  statement would mean estimating  diagrams where the
photon is radiated from internal lines. We leave that investigation
to a future paper.
\newpage
\section{Under the spell of the Coulomb peak}

Pionic bremsstrahlung at very small momentum transfers, {\it i.e.}
 in the Coulomb region,
 is of special interest
since it is there one can hope to extract the pion polarisability.

In the Coulomb region the transverse momentum transfers are so small
they can safely be neglected in the propagators of
eqs (\ref{Propagator1}) and (\ref{Propagator2}).
Furthemore, as explained above,  in this region the
Coulomb contributions dominate
the form factors ${\mathcal F}_{rad}$ and ${\mathcal F}_{pol}$,
and both may be replaced by $f_C(E,\bmath{q}_{\bot})/E$ from eq.(\ref{Point-cross-final}).
After some straightforward simplifications we get the cross section
distribution
\begin{equation}
\frac{\textrm{d} \sigma}{\textrm{d}^2q_{2\bot}  \textrm{d}^2p_{2\bot} \textrm{d} x}
= \frac{4Z^2\alpha^3}{\pi^2m_{\pi}^4}
 \Bigg[ \frac{\bmath{q}_{1\bot}^2}{(\bmath{q}_{1\bot}^2+q_{min}^2)^2}\Bigg]
  \Bigg[ \frac{1-x}{x^3} \left( 1+\frac{\lambda x^2}{2(1-x)}\right)^2\Bigg]
 \label{Coul-peak-cross}
 \end{equation}
 with $x=\omega_2/E_1$ from eq.(\ref{x-fraction}).

The factor inside the first pair of brackets is typical for Coulomb production.
It has the Coulomb propagator, with the minimum momentum transfer, but
due to the numerator it vanishes
in the forward direction. This last property can readily be seen
from expression (\ref{Coulomb_Born_lab}). In the forward direction,
the pion momenta $\bmath{p}_1$ and $\bmath{p}_2$ are both parallel to the
photon momentum $\bmath{q}_2$. Hence,
$\bmath{p}_1\cdot \bmath{\epsilon}_2 =\bmath{p}_2\cdot \bmath{\epsilon}_2=0$ and
  the ${\mathcal M}$-amplitude vanishes.

The factor inside the second pair of brackets contain the dependence on
the pion polarisability. Since from chiral-Lagrangian theory, eq.(\ref{lambda-def}),
we expect $\lambda\approx-0.01$, this dependence is very weak. Let us define
$R(x)$ as
\begin{equation}
  R(x)=
   \left|1+\frac{\lambda x^2}{2(1-x)}\right|^2 \ .
\end{equation}
Suppose then that the bremsstrahlung photon carries half of the energy
of the incident
pion. This gives $R(0.5)=0.99$, and a tiny  1\% effect from
the polarisability. To make a difference, the photon must take nearly
all the energy of the incident pion. As an example  $R(0.95)=0.78$,
a healthy 20\% effect.
 But, increasing the $x-$value implies
according to eq.(\ref{Coul-peak-cross}) at the same time diminishing
the cross section. Going from $x=0.5$ to $x=0.95$ means a reduction
in cross section by a factor of 100. We conclude
that it is possible, but certainly very difficult,
to measure the pion polarisability in pion bremsstrahlung experiments.

Our result is at variance with that of Antipov  {\it et al.}\cite{5}.
In ref.\cite{12} a formula for the factor $R$ is given. It differs from
ours in that only the term linear in $ \lambda$ is kept, and it comes
with a different factor. \\[2ex]

\noindent
{\bfseries Acknowledgements}. I would like to thank Barabara Badelek for
drawing my attention to the
importance of pionic bremsstrahlung.

\newpage
\section{Appendix}
In order to estimate the  size of
the nuclear contributions we calculate the corresponding forward
amplitudes for uniform nuclear mass and charge distributions.
A typical choice of  nuclear radius parameter is
\begin{equation}
	R_u=r_0 A^{1/3}
\end{equation}
with $r_0=1.1$ fm.
The normalised uniform density is then
\begin{equation}
	\rho(\bmath{r})=\frac{3}{4\pi R_u^3}\,\theta(R_u-r)\equiv\rho_0\theta(R_u-r)
\end{equation}
so that the mass and charge distributions become  $\rho_A(\bmath{r})=A\rho(\bmath{r})$ and  $\rho_Z(\bmath{r})=Z\rho(\bmath{r})$.

The forward elastic {\it nuclear amplitude}, void of
 Coulomb distortion, is according to eq.(\ref{fCN-new})
\begin{equation}
	f_N(E,0)= ik\int_0^{R_u}b\textrm{d} b\, \big(1-\exp[-\half\sigma' T_A(b)]\big)
	\label{Forw-nucl-value}
\end{equation}
with $T_A(b)=2A\rho_0R_u\sqrt{1-b^2/R_u^2}$. As always $\sigma'=\sigma(1-i\alpha)$,
with $\sigma$ the pion-nucleon total cross section
and $\alpha$ the phase of the forward elastic pion-nucleon scattering amplitude.
In terms of the parameter
\begin{equation}
	\xi= \frac{3\sigma'}{4\pi r_0^2} A^{1/3}
\end{equation}
we get
\begin{equation}
	f_N(E,0)= ikR_u^2\left[ \frac{1}{2}- \frac{1}{\xi^2}
	+e^{-\xi}\left(\frac{1}{\xi} +\frac{1}{\xi^2}\right)\right] \ .
\end{equation}

The forward {\it polarisability amplitude}, void of
Coulomb distortion, is according to eq.(\ref{fCP-new})
\begin{equation}
	f_{P}(E,0)
	   =-2 \pi \alpha E
    \int_0^{\infty}b\textrm{d} b\, \left[ \int_{0}^b b'\textrm{d} b' \,T_Z(b')\right]
     \left( 1- \exp[-\half \sigma' T_A(b)]\right)
\end{equation}
A straightforward integration gives
\begin{equation}
	f_P(E,0)= -\alpha Z E R_u^2\left[ \frac{3}{10}- \frac{1}{\xi^2}
	 + \frac{24}{\xi^5}
	-e^{-\xi}\left(\frac{24}{\xi^5} + \frac{24}{\xi^4}+ \frac{12}{\xi^3}
	+\frac{3}{\xi^2} \right)\right].
\end{equation}
The scale factor  $\alpha Z$ in front makes $f_P$ smaller than $f_N$

If we take a cross section $\sigma=25$ mb, and $\alpha=0$,
then the numerical parameter is $\xi=0.49A^{1/3}$.
\newpage

redpajama_set_name: RedPajamaArXiv


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Harold in the Land of Jazz
Harold in the Land of Jazz by Bart MendozaDecember 2022
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by Bart MendozaDecember 2022
Harold Land, 1928-2001
While San Diego hasn't been thought of as much of a jazz town until recently, the truth is that many famed jazz-era musicians got their start here, from Arthur Blythe to the Liggins Brothers. Even among such illustrious company, it's clear that one of the most important jazz players ever to emerge from our town is saxophonist Harold Land.
Born on December 12, 1928, in Houston, Texas, Land arrived in San Diego in 1933, at the age of five. His family lived at 1703 Imperial Ave., and he found his love of music early. He attended Memorial Jr. High in Logan Heights and then San Diego High School, graduating in 1946. According to his wife Lydia, "He was in the San Diego High School orchestra, but jazz was his love. He'd had piano lessons, but after he heard Coleman Hawkins, a saxophone was all he wanted to play. When he was 16, he was given a tenor saxophone. Mrs. Land recalls, "Harold had a music teacher who was very strict. Everything had to be a certain way, so for fun, whenever the teacher would leave the room, he would let go with music the way he wanted to play it, taking the same songs and rearranging them." He had just graduated when a friend, bass player Ralph Houston, helped him join the Musician's Union, setting him on the path toward becoming a world-renowned musician.
Land was influenced by other famed saxophonists of the day, including Lucky Thompson and especially Charlie Parker, and became part of the house band at the Creole Palace in downtown San Diego as a member of Fro Brigham's group. "During these jobs my closest friend and musical colleague was the drummer, Leon Petties," Land remembers. Quoted by Leonard Feather in the liner notes to Land's own 1959 album, The Fox, he spoke of his days in the club's small combo. "We played the floor show and jazz sets too. Sometimes men like Hampton Hawes, Teddy Edwards, and Sonny Criss came down from L.A. and worked with us. This provided a great stimulus."
San Diego's Creole Palace, a hot spot for black entertainment in the '20s, '30s, and '40s, at Third and Market St. Photo: San Diego Historical Society.
Though the Creole Palace was a mainstay, Fro Brigham's band played many other venues. "I was a jitterbugger when I met Harold at the Club Romance in 1949," says Mrs. Land. "That club was just two blocks south of the Creole Palace." Of the band at the time she says, "They played all the jazz, well, really bebop, that they could in a set, and all the jitterbuggers would be there. People just loved Fro's voice and wanted to dance."
On April 25th of that year the band, under the moniker the Harold Land All Stars, cut four songs at Savoy Records in Los Angeles, resulting in the regional hit "San Diego Bounce" (Regent 1020) when released in 1950. The song also proved to be a huge hit in Jamaica, where it was bootlegged under the titles "Downbeat Shuffle" or "Coxsone Shuffle." The other three songs, recorded at the session, would have to wait until the late seventies to finally see the light of day on a Savoy Records anthology, Black California.
Land and Petties soon left the Creole Palace to work on the road, first spending a year in a group led by guitarist Jimmy Liggins and then in the band of his slightly more famous brother, Joe "Honeydripper" Liggins. Although Land considered his rhythm-and-blues road experience invaluable, he was soon back at the Creole Palace, though by 1954 he had moved to Los Angeles.
Mrs. Land says, "We lived in San Diego until 1954, and our son was born there. We left San Diego when he was four and not long after that Harold joined up with Max Roach."
Following a succession of menial jobs, close friend flutist Eric Dolphy invited Land to play a jam session at Dolphy's house. Both Clifford Brown and Max Roach came to check out Land for their musical projects on Dolphy's recommendation. "Eric had known me since the San Diego days and after I moved to L.A., we became good friends," Land says in that interview. "He was beautiful. Eric loved to play anywhere, any hour of the day or night. So did I." Land passed the impromptu audition and was soon a rising star in the jazz world, recording enough material to appear on the pair's 16 albums (including reissues) over the years. He left the employ of Brown and Roach in 1956 due to a family illness but continued to tour, notably with Curtis Counce.
More important, he began to play sessions and went on to become one of the leading horn players of his day. He's on literally dozens of the greatest jazz sides ever released. Just check out this roll call: five discs with Bill Evans, 13 with Dinah Washington, six with Thelonious Monk, 12 with Bobby Hutcherson, four with Wes Montgomery—and that's just the tip of the iceberg. It's an incredible discography, which includes countless recording sessions from the likes of the Platters, Sam Cooke, Ella Fitzgerald, Art Farmer, Donald Byrd, and many, many more. Notably, Land made the acquaintance of trumpeter Jack Sheldon (later band leader for The Merv Griffin Show) in 1957, playing on his album Jack's Groove.
As a solo act he signed to Contemporary Records in 1958, releasing three highly acclaimed albums in quick succession: 1958's brilliant Harold in the Land of Jazz and Grooveyard, then The Fox on the small Hifijazz label in the year that followed. Contemporary Jazz records re-issued the album in 1969. He next surfaced on Jazzland Records with a pair of classics: West Coast Blues (1960) and Eastward Ho! Harold Land In New York (1960).
Hear Ye was next, seeing Land as co-group leader with Red Mitchell. It was released by Atlantic in 1961 and has been re-issued six times since, including one in 1967 under the "hip" title And Keep on Swinging. A series of indie releases followed, all stellar. Over the next four decades he appeared on every jazz label of note. The year 1963 saw the release of Jazz Impressions of Folk Music on Imperial and 1967 had The Peace-maker on Cadet, while 1969 found Take Aim issued by Blue Note.
It was during this time frame that several rock luminaries let their love of Land's music be known. On July 25, 1969, prog-rock pioneers Yes included a tribute tune called "Harold Land" on their debut album. When asked about the many cover versions of her husband's music, Mrs. Land replies, "Harold wrote a lot of music," says Mrs. Land. "It's hard to keep track of everything. There have been so many re-issues, especially since CDs came out. And then they change the names of things," she says of the record labels' practice of endlessly repackaging an artist's catalog. "But we do get statements, so we know what's out there."
Land continued to tour, including a stint in Las Vegas as star player with Tony Bennett. He also appeared on all the talk shows of the day including The Tonight Show, The Merv Griffin Show, and The Mike Douglas Show. 1971 saw a pair of releases by Land for Mainstream Records: A New Shade of Blue, and Choma. It also saw the initial release of Damisi, an album with a tricky history. It would be reissued in 1972, '74, and '91 (at least), with each issue containing a slightly different choice of songs. You need the 1991 CD re-issue to get it all.
Next, Land worked on a co-band leader production with Blue Mitchell, releasing Mapenzi for Concord Jazz in 1977. It was followed by Live at Junk in 1980, a release only available in Japan, the same year he joined the Timeless All-Stars, which included Hutcherson, Billy Higgins, Cedar Walton, Curtis Fuller, and Buster Williams. Xocia's Dance on Muse came in 1981, with A Lazy Afternoon on the indie Postcards label released April 1995.
Unfortunately, that would be his last release for seven years. He didn't release an album of new recordings again until 2001's Promised Land on Audiophoric. Sadly, Land passed away on July 27, 2001, but he remained fond of San Diego. "We would return fairly often," says Mrs. Land. "He would play there whenever he could, like when he would play the Athenaeum in La Jolla or even the Summerhouse Inn, for two weeks at a time. He loved it."
Reprinted from the San Diego Troubadour, December 2003.
Mod Revivalists the Trebels to Reunite for 40th Anniversary Show
Sephardic Dance and Music


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Nourishes and hydrates with rich botanicals of primrose, linseed and borage.
After cleansing, toning and applying serum of choice, moisturize in the morning for daily protection.
Tips: Warm between fingertips for effortless application.
Inactive Ingredients: Aloe barbadensis (organic aloe juice/jus d'aloès bio)*, cocos nucifera (organic coconut oil/huile de noix de coco bio)*, pyrus malus (organic apple juice/jus de pomme bio)*, vitis vinifera (organic white grape juice/jus de raisin blanc bio)*, caprylic/capric triglyceride†, sorbitan stearate, ricinus communis (castor seed oil /huile de graines de ricin), polyglyceryl-10 laurate, magnesium sulfate, helianthus annuus (organic sunflower seed oil/huile de graines de tournesol bio)*, rosa canina (organic rosehip fruit oil/huile d'églantier bio)*, camellia sinensis (green tea leaf extract/extrait de feuilles de thé vert), butyrospermum parkii (organic shea butter/beurre de karaté bio)*, simmondsia chinensis (organic jojoba seed oil/huile de graines de jojoba bio)*, oenothera biennis (organic evening primrose oil/huile d'onagre bio)*, linum usitatissimum (linseed seed oil/huile de lin bio), borago officinalis (organic borage seed oil/huile de graines de bourrache bio)*, laminaria ochroleuca (kelp extract/extrait de varech), ubiquinone (CoQ10), thioctic acid (alpha lipoic acid/acide alpha-lipoïque), dimethylaminoethanol (DMAE), tocopherol (Vitamin E/vitamine E), magnesium ascorbyl phosphate (Vitamin C/vitamine C), sodium hyaluronate†, phenethyl alcohol, ethylhexylglycerin†, litsea cubeba (may chang oil/huile de chang mai), cinnamomum camphora (ho wood oil/huile de camphre).


text:
Home / Press room
Ingeteam launches INGEPREDICT: a 360º solution for comprehensive predictive maintenance in the energy and industrial sectors
INGEPREDICT is Ingeteam's new tool that makes it possible to combine all predictive maintenance products and services in a single brand, directed at increasing production and extending the service life of assets at industrial and renewable energy generation plants. INGEPREDICT facilitates the early ...
Ingeteam at EURASIA RAIL 2021
Ingeteam will soon participate in Eurasia Rail 2021, where the main companies in the railway sector will meet, and which will take place in Istanbul from 25th to 27th November. On this occasion, you will be able to find us at Stand A542 (Hall A), where we wil...
Ingeteam to supply its technology for the largest solar farm in Australia
This is stage 1 of The New England Solar Farm. Ingeteam has signed a supply contract with Green Light Contractors Pty Ltd. (subsidiary of Elecnor S.A.) for what is set to be, once completed, the largest solar farm in Australia. The New England Solar Farm is being developed by...
Ingeteam is getting ready to exhibit at Intersolar Europe
Ingeteam is set to exhibit the company's very latest products and O&M services for the solar power and energy storage sectors. The company will showcase its new central inverter featuring 1500V technology, and its lifetime extension tool, Ingeboards, at booth B5.430. Ingeteam will...
Ingeteam adapts its string solar inverters to the new higher power PV panels
Ingeteam has adapted its three-phase string inverter models according to the new photovoltaic panel technologies, which in recent times have been increasing their current and power levels. Ingeteam's three-phase inverters INGECON SUN 20TL M, INGECON SUN 33TL M, INGECON SUN 100TL PRO and INGECON SUN ...
Ingeteam makes its largest supply of solar inverters in the US
This is the first supply contract that Ingeteam has signed with Swinerton Renewable Energy, one of the leading EPC companies in the USA. The 350 MW supply is divided into two photovoltaic plants, 100 MW and 250 MW, that the company is building in California. Ingeteam Inc., a manufactu...
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Automation Devices
O&M Services
Solar Photovoltaic Power


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Irish, British & European politicians defend anti-abortion laws in Ireland
By John Smeaton, executive director, Society for the Protection of Unborn Children (SPUC)
John Smeaton
Today in Northern Ireland's Parliament Buildings, Stormont, a coalition partnership of politicians from Northern Ireland, the Republic of Ireland, Britain and Europe stressed the vital importance of not decriminalising abortion in the Republic of Ireland and of upholding the 1861 Offences against the Person Act, sections 58 & 59, which prohibit abortion.
The coalition included Jim Wells MLA [Member of the Legislative Assembly], Danny Kennedy MLA, Paul Givan MLA, Pat Ramsey MLA, Jim Walsh a member of the Irish Senate, along with Ian Paisley Junior MP, Jeffrey Donaldson MP and former MEPs [Members of the European Parliament] Dana Rosemary Scallon and Kathy Sinnott, and pro-life leaders Bernie Smyth, of Precious Life, and Liam Gibson of the Society for the Protection of Unborn Children. There were messages of support from Edwin Vassallo MP of Government Party of Malta, from British Parliamentarians, Lord David Alton, Lord Windsor, and Fiona Bruce MP, and from European parliamentarians Luca Volonté MEP, and Diane Dodds MEP.
The message from the meeting of politicians was:
Under the 1861 Offences against the Person Act, sections 58 & 59 ban abortion in Northern Ireland and the Republic of Ireland.
The role of Government is to uphold the Law.
The weakest and most vulnerable in society must not be systematically dehumanized by catchy slogans, clever marketing, slick advertising and aggressive lobbying.
Senator Jim Walsh stated that abortion is barbaric. Jeffrey Donaldson MP, said the first duty of a politician is to protect the vulnerable and no one is more vulnerable than the unborn. Ian Paisley Jnr. MP, stated that Dr Ian Paisley (senior) fully supported this core group initiative.
Pat Ramsey MLA said that the Social Democrat and Labour Party is a pro-life party and defends the right to life of the unborn. Paul Givan MLA, stated that the pro-life position unites communities and Sinn Fein [another Irish political party] must reflect on their opposition to legislation designed to protect unborn children. Danny Kennedy MLA, said the pro-life point of view represents the majority. Former MEP Kathy Sinnott said that politicians must move out of their comfort zones to defend the right to life and if a woman's life is in danger then she should be in a hospital and not an abortion clinic. Dana Rosemary Scallon said that all values are worth defending and at this moment "we must defend the value of life since the fundamental right to life is the basis of all other rights".
Categories icon Legislation
Tags icon anti-abortion laws, Ireland, SPUC
Terri Schiavo-Type Patients May Feel Pain
The Gender Equality Argument for Legalized Abortion


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Q: R script file encoding (R Studio) Which file encoding do I have to use to be able to save this vector (Matching complex URLs within text blocks (R)) correctly in a R script? The special characters and Chinese signs seem to make things somehow complicated.
x <-   c("http://foo.com/blah_blah",
        "http://foo.com/blah_blah/",
        "(Something like http://foo.com/blah_blah)",
        "http://foo.com/blah_blah_(wikipedia)",
         "http://foo.com/more_(than)_one_(parens)",
         "(Something like http://foo.com/blah_blah_(wikipedia))",
         "http://foo.com/blah_(wikipedia)#cite-1",
         "http://foo.com/blah_(wikipedia)_blah#cite-1",
         "http://foo.com/unicode_(✪)_in_parens",
         "http://foo.com/(something)?after=parens",
         "http://foo.com/blah_blah.",
         "http://foo.com/blah_blah/.",
         "<http://foo.com/blah_blah>",
         "<http://foo.com/blah_blah/>",
         "http://foo.com/blah_blah,",
         "http://www.extinguishedscholar.com/wpglob/?p=364.",
         "http://✪df.ws/1234",
         "rdar://1234",
         "rdar:/1234",
         "x-yojimbo-item://6303E4C1-6A6E-45A6-AB9D-3A908F59AE0E",
         "message://%3c330e7f840905021726r6a4ba78dkf1fd71420c1bf6ff@mail.gmail.com%3e",
         "http://➡.ws/䨹",
         "www.c.ws/䨹",
         "<tag>http://example.com</tag>",
         "Just a www.example.com link.",
         "http://example.com/something?with,commas,in,url, but not at end",
         "What about <mailto:gruber@daringfireball.net?subject=TEST> (including brokets).",
         "mailto:name@example.com",
         "bit.ly/foo",
         ""is.gd/foo/"",
         "WWW.EXAMPLE.COM",
         "http://www.asianewsphoto.com/(S(neugxif4twuizg551ywh3f55))/Web_ENG/View_DetailPhoto.aspx?PicId=752",
         "http://www.asianewsphoto.com/(S(neugxif4twuizg551ywh3f55))",
         "http://lcweb2.loc.gov/cgi-bin/query/h?pp/horyd:@field(NUMBER+@band(thc+5a46634))")

I appreciate any help.

A: Running your example,
source('file.R', encoding="unknown")

works fine and saving as R object and reloading works as well:
 save(x, file='kk.Rd')
 load('kk.Rd')

You can get all different encodings with iconvlist() and test them all, for example:
vals <- lapply(iconvlist(), function(x)
                      tryCatch(source('file.R', encoding=x),
                               error=function(e)return(NULL)))

with file.R being your script, and then
iconvlist()[which(!sapply(vals, function(x)is.null(x)))]

gives you all encodings where no error was thrown while loading.
Does this help?

redpajama_set_name: RedPajamaStackExchange


text:
It's been raining off and on "Cat's & Dogs" all day, and that kind of suits my mood today. There is absolutely NO joy in Mudville, a.k.a. Red Sox Nation, or for the foreseeable future. What a total disaster this baseball season has been for those of us who count ourselves as fans of the Sox. The fall of the Buckner, so to speak, was the year I moved from New York to Boston. As a long time, and long suffering, Mets fan I didn't know who to root for 'cause I liked the Sox as well. That was a disaster of epic purportions, but this was one orders of magnitude worse. Anyhow, it's really got me down�
Trying to keep moving right along� "The leaves on the trees they are fallen'�" And if we get much more rain, I'm not sure what's going to happen to the Leaf peeper Season. 5-6 years ago we had the rains come through right as the leaves were switching, and they all fell off & blew away. Needless to say it wasn't too pretty. So let's hope that we don't get a wind storm and that doesn't happen this year. Our weakened economy would definitely NOT like that.
We're having some absolutely terrible mosquitoes right now. YUP, that's right - mosquitoes in the end of September. As best we all can figure, it's because of the rains that Irene brought, coupled with the very warm temps - sometimes in the low 80's! I have some friends who live out in Brownfield and they say it's brutal. It's been bad enough at Humphrey's that we've been pouting on bug dope. Tho there was a cool snap a couple of weeks ago, it really didn't frost down here in the Valley. I don't usually find myself hoping for an early frost, especially since I still have tomatoes on the vine. However this year it can't come soon enough.
Hunting season started a couple of weeks ago! It's the time of year when you really don't want to be poking around in the deep woods without the orange! Right now it's the archery season, but shotgun and rifle will be here before you know it. Over the years I've been riding my mountain bike way out by the Moats and up near Black Cap and occasionally heard shots, needless to say making me pretty darn nervous. For those of you into back-country hiking and climbing I recommend you be aware. Here's the current dates from the NH State Wildlife site. the actual link is here:
http://www.wildlife.state.nh.us/Hunting/hunting_dates_and_seasons.htm
Sept. 15 - Dec. 15: Deer/archery (Note: September 15-30, archers may only take legally antlered bucks statewide; archery season closes on Dec. 8 in WMU A)
Sept. 15 - Dec. 15: Fall turkey/archery
Oct. 10 - Oct. 14, 2011: Fall turkey/shotgun (in certain WMUs only); Monday - Friday
Sept. 2011 - March 2012: Small game and furbearers/dates vary by species and region
Oct. 1 - Dec. 31: Pheasant
Oct. 15 - Oct. 23, 2011: Moose (by permit only)
Oct. 22 - 23, 2011: Youth deer-hunting weekend
Oct. 29 - Nov. 8, 2011: Deer/muzzleloader
Nov. 9 - Dec. 4, 2011: Deer/regular firearms (closes November 27 in WMU A)
Another New Route At Humphrey's Ledge:
Yep, here's yet another new route at Humphrey's Ledge. This one is on the area just right of Shifty Eyes. It's surprising how if you're looking you can still find interesting lines in a place we all thought was tapped out. George Hurley is amazing at this. Just check out his lines on and above the North End of Cathedral. In the case of Granite State, Joe & Judy Perez noticed this line a while back. We TR'ed it a couple of times over the past few weeks and they finished it off on Monday. The name comes from the outline of a colder that I trundled off the top of the buttress one afternoon. It's actually one whole side of the buttress! Too bad 'cause it was one side of a splendid finger crack! Oh well�
I think that the climbing is fun, check it out.
Granite State (5.8):
Directions: Hike up the hill to the cliff and go left about 50'. When you get to the Shifty Eyes face, the climb is located on a slight buttress to the right of Shifty Eyes and Undertow. A large block on the ground that looks a little like the state of New Hampshire marks the start of the climb.
Description: The climb is characterized by steep face climbing that requires good balance and body position at the first two bolts.
Pitch 1: Begin climbing the route at the shallow mossy groove on the right of the buttress. Good protection can be found in a short horizontal crack to the right of the groove. Climb the center of the buttress to a stance at an obvious horizontal crack (gear). Step left and up to the first two bolts. Above the two bolts move right to the third bolt and up a large block to its top. 50'
Gear: Small and medium cams
Descent: Rappel from double ring anchors on the wall above the top of the block
First Ascent: Joe Perez, Judy Perez, Al Hospers, Jeff Lee, September 26, 2011
While we were waiting on Joe to put in the bolts on Granite State, Jeff Lea led my new climb Can YOU Believe it? He felt that it was as 5.8 as I had thought. It's always nice when someone confirms what you thought about a new line. When you're working on something like that it's hard to tell what it will be for someone else.
All Cycling Aside:
I was up riding by the Tent Boulder behind Whitehorse a couple of days ago. On the way down, just before you get to the steep sidehill that has recently been rerouted, we noticed an interesting old logging road heading downhill. We gave it a shot and it is actually a brilliant piece of singletrack that will take you all the way down to the main logging road that runs from Joe's Alibi up to the Carroll Reed Trail. If you ride, check it out. It's tres-cool.
Instant Bug Report:
Depending on where you are the mosquitoes are bad to horrendous. I'm not changing the BugCON level, but seriously consider bring some dope, besides the brother-in-law, with you if you're gonna be out in the woods.
There are old climbers, there are bold climbers, but there are no old bold climbers!


text:
The Panama City POPS Performs Windborne's "Music of the Eagles: A Rock Symphony"
PANAMA CITY BEACH, FLA., - Bridging the gulf between rock 'n roll and classical music, the Panama City POPS Orchestra performs Windborne's Music of The Eagles at Aaron Bessant Park Amphitheater in beautiful Panama City Beach, Fla. on Saturday, September 14, 2013. The concert will kick off at 7:30 p.m. and is free to the public.
The performance is a perfect chance for concert-goers to experience their favorite Eagles' songs backed by a full orchestra at Panama City Beach's spectacular Aaron Bessant Park Amphitheater, a $2.6 million, 7,500-person open-air venue which opened in March 2013.
"The new amphitheater is a true gem, where locals and visitors alike can enjoy amazing performances like this one, while taking advantage of our destination's incredible outdoor surroundings," says Dan Rowe, president and CEO of the Panama City Beach Convention and Visitors Bureau.
Comprised of 65 musicians, The Panama City POPS Orchestra is well known for its dynamic performances of classical and current music. Backing rock musicians performing the music of the Eagles, the orchestra will be led by guest conductor Brent Havens and feature vocalists including Panama City Beach local Terry Brock (also a former vocalist for the rock band Kansas), Glenn Delaune (38 Special, Foghat, Kansas) and John Hines (The Hines Brother's Band).
"The music itself is one thing, but these singers, along with the background singers, more than capture the spirit of the original songs," says Havens.
Locals and visitors are encouraged to bring blankets and chairs to enjoy an unforgettable evening of music under the stars. Coolers are not permitted. For more information www.panamacitypops.org.
TWEET THIS! The @PanamaCityPOPS bring The Eagles' music to @PCBeach Sept. 14