RADIATIVE CORRECTIONS FOR (e, e'p) COINCIDENCE EXPERIMENTS

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RADIATIVE CORRECTIONS FOR (e, e’p) COINCIDENCE EXPERIMENTS

E. Borie, Dieter Drechsel

To cite this version:

E. Borie, Dieter Drechsel. RADIATIVE CORRECTIONS FOR (e, e’p) COINCIDENCE EXPERIMENTS. Journal de Physique Colloques, 1971, 32 (C5), pp.C5b-287-C5b-289.

�10.1051/jphyscol:19715152�. �jpa-00214732�

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RADIATIVE CORRECTIONS FOR (e,elp) COINCIDENCE EXPERIMENTS E. Borie * and Dieter Drechsel

Institut fur Theoretische Physik der Universittit Frankfurt/Main

* Fellow of the Alexander von Humboldt-Stiftung

Résumé : Dans cet article, nous présentons une formule de queue radiative pour l'analyse des expé- riences (e, e 1 N) en coïncidence. On calcule d'abord en première approximation de Born l a section efficace différentielle en énergie e t angle pour toutes l e s particules finales pour l e rayonnement de freinage associé avec l'émission d'un nucléon. Cette formule e s t ensuite intégrée s u r tous l e s angles du photon dans l'approximation de pic.

Abstract : In this paper, a formula for the radiative tail, suitable for use in the analyses of (eeTN) coincidence experiments is derived. We f i r s t calculate the c r o s s section differential in the energies and angles of al1 final particles f o r bremsstrahlung associated with the emission of a nucleon, in f i r s t Born approximation. This c r o s s section is then integrated over the angles of the unobserved photon, using t h e peaking approximation, t o give an expression f o r t h e radiative tail in nucleon emission processes.

As in al1 electron scattering processes, the radia- inelastic scattering without detection of a nucleon.

tive corrections a r e expected t o be important when a In addition, corrections due t o emission of a hard nucleon is detected in coincidence with the final electron. photon of energy Ir, in addition t o the proton, a s shown It is t r u e that one thus avoids the considerable difficul- in Fig. 1 , must be considered. We consider only brems- t i e s with background that a r i s e f r o m the l a r g e radiative strahlung f r o m t h e electron. This proeess is expected tail f r o m the elastic peak. However, the inelastic radia- t o dominate, since the electron m a s s is s o much smaller tive tail of the continuum levels can still contribute, and than the other m a s s e s involved. We concentrate only on the usual radiative correction f o r inelastic scattering[l] photon emission in the field ot the target nucleus. Radia- arising f r o m the emission and absorption of virtual pho- tive l o s s e s corresponding t o straggling in t h e target tons, and the emission of r e a l soft photons, must still (t2 effects) will not be discussed here. But since they do be applied. This correction is given t o lowest o r d e r by not depend on t h e specific nuclear process being studied,

d g = d G p - 5 ) ₍₁₎ but only on t h e electron kinematics, it is expected that where dro is the uncorrected c r o s s section and

5 _v[(th 55 _{( A E F}-9)()(P. ₆ 9yhl- r ) + ₁₈3

these effects can be treated exactly a s they a r e when only the electron is detected. To obtain a formula useful

- .

+ '

&

t k ^t$ - L ~ ( c ~ ~ L ; Q

2" El,

11

^{( 2 )} for the analysis of (e, e'N) coincidence experiments, it is

This correction depends only on the electron necessary to calculate the c r o s s section differential in uinematics, and i s independent of what happens in the the energy and angles of the unobserved photon. This target. Thus it is exactly the s a m e as the correction for l a s t is done by using the peaking approximation. The

Fig. 1 Diagrams f o r bremsstrahlung accompanying nucleon emission

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19715152

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E. BORIE AND D. DRECHSEL

details will appear in Nuclear Physics

121

and will just a s they a r e f o r the c a s e of ordinary (e, e t ) experi- therefore not be given here. The final result is : ments.

The c r o s s section dc (h - k , E t 1 JI plop) appears in the formula f o r the radiative tail. This means that one must t,-k.,EZiqtl know this c r o s s section f o r al1 values of the incident

ZE, dqG (

c l n , d % d n p d e ~ energy between threshold for proton emission and E,

Z E ~ d & ( ~ * , & ~ + k ~ q , t p # ' p ) (this is of course an improvement over needing t o know

,

( E L + k ) t + ~ : t h

-

(E %+ k)' ^rn ^dn,da,dnp ^dep it f o r &values l e s s than E, ). Since our theoretical

wher e

P. 2

q,

⁼ ^LU + ^4é, ^(E,

+

k ) 5 ; h L

+

^O

qt

⁼ ^'uL ⁺^qe,^(t,

-

^{k )}^{% n t}^2.₂ ^O

u = E, - EL

-

^1'

( 3 ) knowledge of t h e (e, e t p ) process is still somewhat crude, it will be necessary t o perform an unfolding of the spec- t r a , using experimental data taken a t lower incident energies.

In o r d e r to give a n idea of the effect of t h e radiative corrections, missing energy spectra for kinematics

and

is the (e, erN) coincidence c r o s s section without radiative corrections a s given by de Forest. [3] The f o r m fac- t o r s WC, Ws, W and W a r e discussed in Ref. 3. Obser-

1 S

v e that t h i s formula is very s i m i l a r to the peaking t e r m s in the expression f o r t h e radiative tail for inelastic scattering a s given by Maximon and Isabelle. [4] Thus, to the extent that the peaking approximation is valid, the radiative corrections t o (e, erp) can be handled just as they a r e f o r the c a s e of ordinary (e, e'p) can be handled

similar t o those of t h e Saclay experiment

C 5l

(E, ²SooMeV, O= 52.7' LP = 8% W ~ V ) ep varied with E, s o a s t o keep 117-3 ) fixed and ( < ~ ~ = ~ ( c o p l a n a r experiment)), using the quasielastic model f o r the nucleon emission process, and a very simple single particle harmonic oscillator shell model (but with phenomenolo- gical shell binding energies taken f r o m experiment) t o describe the nuclear s t r u c t u r e ,were computed. The r e s u l t s a r e shown in Figs. 2,3. In each figure the dashed curve is computed directly f r o m t h e formulas given in Ref. 3 , and the solid curve is obtained by multiplying t h e

computed c r o s s section by 4 - , then adding t h e inte- g r a ï of €9

1

³³ over k f r o m be t o E,

-

^EL-^{t P .}

Even though t h e model used is somewhat crude, certain qualitative features exhibited by the curves a r e probably reproduced in the exact c r o s s sections. Peaks a r e reduced in height, by about 30 %, f o r emission of a valence shell proton, and the c r o s s section is increased by a factor 3-4 a t l a r g e missing energy. Peaks corresponding to emission of an inner shell nucleon tend t o be washed out (due to a filling in of the "valley" between the peaks) but can still be observed a s shoulders if the shell is suffi- ciently narrow.

REFERENCES

[ ¹¹ Maximon (L. C. ), NBS Report, 9864, 1968,

-

_{45, 365.}

unpublished.

[ 2 ] Borie (E.) andDrechsel (D.), t o be published in _{[ 4 ]} Maximon (L. C.) and Isabelle (D. B. ), Phys. Rev.,

Nuclear Physics. 1964,

136,

B 674

131 de Forest (T. ), Jr. , Annals of Physics, 1967,

151 Mougey (J. ), private communication.

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RADLATIVE CORRECTTONS FOR (ee'p) COINCIDENCE EXPERIMENTS

- - - - _ _ _ _

O 25 5b 75 1 5

' O 0 e4 - E L -

5

^;fi&)

Fig. 2 Missing energy spectrum for 12c in arbitrary units

Fig. 3 Missing energy spedrum for 4 0 ~ a in arbitrary units