Fortschritte der Physik / Progress of Physics: Band 27, Heft 5 1979 [Reprint 2021 ed.] 9783112522684, 9783112522677

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FORTSCHRITTE DER PHYSIK HERAUSGEGEBEN IM AUFTRAGE DER PHYSIKALISCHEN GESELLSCHAFT DER 1 >EUTSCHEN I) EM O kRATISCH IiN R F.I'U BLIk VON F. K ASC II LU II N\

LÖSCHE, R. RITSCHL UM) R. ROM PK

HEFT 5 • 1979 • BAND 27

A K A D E M I E - V E R L A G

EVP 10,- M 31728

•

B E R L I N

BEZUGSMÖGLICHKEITEN Bestellungen sind zu richten — in der DDR an das Zeitungsvertriebsamt, an eine Buchhandlung oder an den AKADEMIE-VERLAG, DDR - 108 Berlin, Leipziger Straße 3—4 — im sozialistischen Ausland an eine Buchhandlung f ü r fremdsprachige Literatur oder an den zuständigen Postzeitungsvertrieb — in der BRD und Westberlin an eine Buchhandlung oder an die Auslieferungsstelle KUNST U N D WISSEN, Erich Bieber, 7 Stuttgart 1, Wilhelmstraße 4—6 — in Österreich an den Globus-Buchvertrieb, 1201 Wien, Höchstädtplatz 3 — in den übrigen westeuropäischen Ländern an eine Buchhandlung oder an die Auslieferungsstelle KUNST U N D WISSEN, Erich Bieber GmbH, CH - 8008 Zürich/Schweiz, Dufourstraße 51 — im übrigen Ausland an den Internationalen Buch- und Zeitschriftenhandel; den Buchexport, Volkseigener Außenhandelsbetrieb der Deutschen Demokratischen Republik, D D R - 701 Leipzig, Postfach 160, oder an den AKADEMIE-VERLAG, DDR - 108 Berlin, Leipziger Straße 3—4

Zeitschrift „Fortachritte der P h y s i k " Herausgeber: Prof. Dr. Frank Kaschluhn, Prof. Dr. Artur Lösche, Prof. Dr. Rudolf Ritsehl, Prof. Dr. Robert Rompe, im Auftrag der Physikalischen Gesellschaft der Deutschen Demokratischen Republik. Verlag: Akademie-Verlag, D D R - 108 Berlin, Leipziger Straße 3 - 4 ; F e m r u f : 2236221 und 2 2 3 6 2 2 9 ; Telex-Nr. 114420; B a n k : Staatsbank der D D R , Berlin, Konto-Nr. 6836-26-20712. Chefredakteur: Dr. Lutz Rothkirch. Anschrift der Redaktion: Sektion Physik der Humboldt-Universität zu Berlin, D D R - 104 Berlin, Hessische Straße 2. Veröffentlicht unter der Lizenznummer 1324 des Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Republik. Gesamtherstellung: V E B Druckhaus „Maxim Gorki", D D R - 74 Altenburg, Carl-von-Ossietzky-Straße 30/31. Erscheinungsweise: Die Zeitschrift „Fortschritte der Physik" erscheint monatlich. Die 12 Hefte eines Jahres bilden einen Band. Bezugspreis je Band 1 8 0 , - M zuzüglich Versandspesen (Preis für die D D R : 120,— M). Preis je H e f t 1 5 , - M (Preis für die D D R : 1 0 , - M) Bestellnummer dieses Heftes: 1027/27/5. (c) 1979 by Akademie-Verlag Berlin. Printed in the German Democratic Republic. AN (EDV) 57 618

ISSN 0015 - 8 2 0 8 Fortschritte der Physik 27, 209 - 2 6 0 (1979)

Exchange Currents, Isobaric Excitations and the Deuteron H . BATEB

Institut für Radiumforschung und

Kernphysik*)

Universität Wien, Austria

Abstract Some recent attempts to take into account exchange currents and isobaric excitations in the electromagnetic and weak interactions of leptons with the deuteron are reviewed. After a presentation of the relevant theoretical framework the crucial experiments supporting strongly the exchange current ideas are discussed in some detail. Contents Introduction

209

1.1. 1.2. 1.3. 1.4. 1.5.

Definition of currents Single particle currents Exchange currents Low energy theorems and compensation of recoil term 2 nucléon wave functions

211 215 216 224 229

11.1. 11.2. 11.3. 11.4. 11.5.

Thermal neutron proton radiative capture Electrodisintegration of the deuteron Deuteron photo-disintegration Formfactors of the deuteron Weak currents and the deuteron

238 239 243 245 254

Appendix

255

References

256

Introduction The deuteron and its interaction with electrons and photons has been the subject of a vast number of both experimental and theoretical work. The theoretical analysis started with a conventional nonrelativistic Schrödinger description of the bound and scattering states in the two nucléon system and frequently used the conventional reaction theories. Using single particle current operators with conventional (and there*) A-1090 Wien, Boltzmanngasse 3. Österreich 18

Zeitschrift „Fortschritte der Physik", HeitB

210

H . BAIER

fore semiphenomenological) introduced electromagnetic nucleón formfactors one obtained generally qualitatively good fits to low and medium energy data even within such an admittedly crude approach. As examples one should mention the (n, p) capture cross section, the electro resp. photo break up of the deuteron and the electromagnetic formfactors of the deuteron. However quantitative agreement between theory and experiment (especially at high momentum transfer) was not obtained within the conventional approach just mentioned. It became clear that quite an impressive agreement between theory and experiment was possible when (in addition to the nucleonic degrees of freedom) mesonic and nucleonic degrees of freedom are taken into account in a more sophisticated description of the reaction processes mentioned above. Formally this then leads to the introduction of interaction (or exchange) currents in addition to the usual single particle currents and to the explicit introduction of mesonic degrees of freedom in the deuteron wave function. From a theoretical point of view it is furtheremore not clear at all that a nonrelativistic description of the medium energy processes (and of course of the two nucleón system) should be an adaequate representation of the facts. Quite often the interaction effects are introduced in an ad hoc and unsystematical manner as a perturbation to the simple impulse approximation using "best" semiphenomenological nonrelativistic two nucleón wave functions. From recent work one knows however that it is unjustified to construct the two nucleón interaction (and a fortiori the wave function) independent from the construction of the effective projectile deuteron interaction (e.g. the bound state current) operators. Otherwise it would not be easy to understand e.g. the compensation of recoil graph and wave function renormalization often mentioned in the literature and discussed in the present review. Ideally one would start from a relativistic (e.g. field theoretical) description of the projectile deuteron system and then deduce thereof the nonrelativistic approximation in a consistent way. Therefore quite recently field theoretical methods of M A N D E L S T A M (1955) were used to derive bound state currents and the methods of B L A N K E N B E C L E R and S U G A R (1966) and others were applied to derive consistently relativistic and nonrelativistic approximations to the 2- (and few body) Bethe-Salpeter equation and to the relativistic currents just mentionned (see e.g. J A T J S (1976)). Analogous to the electromagnetic interactions exchange currents play an important role in the case of weak projectile deuteron interactions (e.g. muon capture) too. Such processes are therefore discussed in the review together with the electromagnetic exchange effects. The following review brings at first a broad survey of some of the methods used in the treatment of exchange currents and isobaric effects in electromagnetic projectile deuteron interactions and gives then experimental and theoretical conclusions obtained during the last years using the deuteron as a target in some crucial electromagnetic and weak interaction processes. Part I of the paper delivers the theoretical background, starting with a widly used definition of the currents (LI). Relevant Feynman graphs and their evaluation are mentionned briefly. Bound state current operators are then defined following M A N D E L S T A M (1955). The single particle and exchange current densities are then discussed in quite a detailed manner (1.2.—3.). Low energy theorems for electromagnetic and weak currents and the compensation of the recoil term against the wave function renormalization are discussed in 1.4. It follows then a short characterization of the two nucleón wave function used in the reaction work mentionned above 1.5. Conventional aspects are mentionned in 1.5.1. more subtile aspects are reviewed in 1.5.2.—1.5.4. Isobaric admixtures are introduced in 1.5.5. The method of coupled channels and criticism to it is treated in that context. Pert II gives a short discussion of the following experimental work: n + p 2 H + y (II.1.), e- + a H n + p + e- (H.2.), T + 2 H -> n + p (II.3.) e - + m -> e- + 2 H (formfactors of 2 H, H.4.), ¡ir + 2 H 2n + v (H.5.).

Exchange Currents

211

1.1. Definition of currents The following fig. 1.1 symbolizes in the usual perturbation scheme the interaction of a two nucleón system with an external (virtual electromagnetic or weak electronneutrino) field. The circles in the figure summarize the interactions between the nucleons or the nucleons and the external fields respectively. I n low and medium energy range usually only the following approximations (Fig. 1.2.1—1.2.3) to the previous are considered. Fig. 1.2.1 describes the impulse approximation (IA) whereas Figs. 1.2.2 and 1.2.3 give the contribution of the one and two boson exchange to the process considered (Bosons are symbolized by broken lines).

o o o o Fig. 1.1

Fig. 1.2.1

o

o ¿ o o AO Fig. 1.2.2

Fig. 1.2.3

To evaluate the previous graphs detailed models for the propagators and vertex parts have to be introduced. Very often only phenomenological expressions for the vertices on-and off-shell are available. As a matter of fact most of the vertices discussed later on were obtained for on shell processes only. Off shell continuation remains largely incertain. (By off shell we mean off the mass shell: hence for a particle of mass m and four momentum ( p , p0) generally p02 — p2 4= w 2 ). Assuming the single pieces of the graphs to be known, Feynman techniques may be used to p u t things together. The following Figs. 1.3.1—1.3.7 show some of the one boson graphs used in the low and medium energy range (applying time ordered Feynman graphs, time running upwards from bottom to top of the page). Some of the specific 2 boson exchange graphs are given in the Figs. 1.4.1—1.4.4. (Full, full thick and broken lines are symbols for nucleons, nucleon isobars and bosons respectively). As an example we show in Fig. 1.5 the usual boson Feynman graph and all its time ordered contributions. For simplicity in Figs. 1.3, 1.4, 1.5 the circles representing the full particle interaction vertices are suppressed. Usually the names for the graphs given above are the following: 1 Boson exchange (Fig. 1.3.1), seagull graph or catastrophic term (Fig. 1.3.2), pair term (Fig. 1.3.3), wave function renormalization (Fig. 1.3.4), recoil graph (Fig. 1.3.5); (B, B', F) (Fig. 1.3.6, F — y for interaction with photon fields and F = A for interaction with a weak axial vector field; B, B' mean two different bosons); rescattering or isobaric excitation graph (Fig. 1.3.7). Fig. 1.4. gives a model for the 2 boson exchange taking isobaric excitation into account. 18»

212

H . BAIEB

P 1

Q ^

H

Kj

J .

P 2

K2 S

i

1

i

B

B

/ I

Fig. 1.3: Time-ordered 1 boson exchange graphs

—\>

IVW^

1

2

Fig. 1.4: Time ordered 2 boson exchange graphs

Fig. 1.6.1 resp. Fig. 1.6.2 consider the possibility of isobaric excitations in the wave functions of the 2 N system. Starting with the S-matrix element for the following process Fig. 1.7 (IA is considered separately!), one may define the current operator in the one pion (or more generally

213

Exchange Currents

7"— —

^

M

A

+

J

¿ ì k .

T

y Fig. 1.5 : Decomposition ol a covariant Feynrnan graph into time ordered parts

C

E

D

o

1

p

2 Fig. 1.6

Fig. 1.7 1

Boson) exchange approximation Fig.

1.1

(see e.g.

(P1P2 I JP] I P1P2) (2tc)3 d°(Pl +p2 = (2*)-* d*(Pl +p2

+

q-p1>-

CHEMTOB-RHO ( 1 9 7 1 ) ) :

+ q-pl'

-

ft')

p2') |