Study of the f72 ground isobaric analog resonance in the (e, e′p) reaction on 139La and 141Pr

Nuclear Physics A294 (1978) 141-160 ; © North-floUand PtrblLhlng Co ., Anvtpdom Not to be roproduoed by Dhotoprint or miao5lm without wrhtm pmmiaion 5rom the publüha~r

STUDY OF THE f~ GROUND ISOBARIC ANALOG RESONANCE IN THE (e, e'p) REACTION ON ta9Ltt AND ' 4 'Pr JUN-ICHI UEGAKi fand KATSUFUSA SHODA laboratory of Nuclear Science, Tohoku University, Tornizawa, Sendal, Japan Received 10 May 1977 (Revised 23 August 1977) Abstract : Difïerential cross sections and proton spectra around the f,~ 2 IAR lII "'La and "'Pr have been measwed for the (e, e'p) reaction using a broad-range magnetic apectromettr and 100 solid-state detectors. Strengths deduced for these IAR agree with previous data which contradicted the results of the (p, ye) reaction and ß~ecay for the spin-flip type trans~tlOn m' s'La. The proton decay mode through these resonancea was studied by the photon-difference method and also by analysis of isochromats . It has been found that the IAR in the electromagnetic reaction decays through two different kinds of proton channel ; one of these is through the configwation characteristic of the IAS and the other is through an unidentified process .

E

NUCLEAR REACTIONS "'La, "'Pr(e, e'p), E = 14 .3-17 .3 MeV ; measwed do/d~1, E~ ; EP, B p = 125 .3° . ' 39La, "'Pr deduced decay mode for IAR. Natural target .

I.

Illt>~1lCtll)n

The isobaric analog states (IAS) studied with nucleonic beams have provided much information on nuclear structure and reaction mechanisms. However, not many experimental investigations have been made of the IAS by means of the electromagnetic interaction with photon or electron beams because the experimental resolutions with photon or electron beams have usually not been better than those with nucleonic beams. An interesting application of the electromagnetic experiments related to IAS is to compare the E1 matrix element with the first-forbidden ß - matrix element. Fujita t) suggested the relation between these matrix elements to be

Cflmß IPi =

2(T+ 1)Ct7ntrIIAS~,

(1)

where IP) is the parent state ofIAS. Examples of the results ofthe (e, e'p) experiments were given in previous papers z .3 ). With these results, strong enhancements were observed in the spin-flip transitions lg~ -. 2fß lII t 39 La, and also lht -" 2g t in 2 °9Bi, after approximate correction for the interference between the IAS and GDR in the f Present address : Saskatchewan Accelerator Laboratory, University of Saskatchewan, Saskatoon, Saskatchewan, Canada .

142

J. UEGAKI AND K . SHODA

isobaric analog resonances (IAR). Such enhancements disagreed with theoretical studies 4. s) as well as with (p, yo) experiments 6). The ß-decay matrix elements deduced from the ß-decay experiment also showed a discrepancy with (e, e'p) results for the transition mentioned above'). These discrepancies motivated us to repeat the measurements of the (e, e'p) cross section for the same IAR. The present paper describes a study of proton emission modes through the 1f~ IAR in '39La and '4tPr relating to the spin-flip transition lg~ -" 2fß, ( 139La) and the non-spin-flip transition 2d t ~ 2fß (t 4tPr), as shown in fig. 1. The cause of the discrepancy mentioned above is discussed . T,aDR 21.0

i~~~~

T,ODit 20 .4 iiiii/iaiiil

i%4o

~a~21~~-~ T
~I II III I IIr ~r

~ewo I T.aon)~ uso

f ~ I AS

GNPH

t+

stata

GNPH sau.

Ip

1 I~ "s,;: é:iâ

t 1A3

1

8 .22

13eea

Or OA

P ~f I A S f h IAS

9. 3 9

~Î l~j

~

2" .gV~

t.so

14o Ce

Ip

t3s~a

~t z

'4t P r

Fig. 1 . The level diagrams relating the El IAS and parent states . The energies are indicated in units of MeV.

2. Experimental procet~e and results

Targets of t 39La and t4tpr were bombarded with momentum-analyzed electrons (dp/p = 1 .5~) from the Tohoku University 300 MeV linear accelerator. Targets of self-supporting metal foils of natural La ( > 99.5 ~ pure) and natural Pr (> 99.9 pure) were set at an angle of 25° to the beam direction. A magnetic core monitor 60 cm in front of the target was used to measure the electron current. Energy distributions of protons emitted at a lab angle of B = 125.3° were measured with a Browne-Buechner type broad-range magnetic spectrometer e) and a ladder of one hundred Si(Li) solid-state detectors arranged in the focal plane. Details of this system and the data acquisition system have been described in a previous paper ~.

»9~ i4~p~~,

~"P)

143

~° a

0

a ù

.N: 4.

uY ~ aO a ~

LV

.~

m

~- .C G

W

4p .+ . . ag 3~,d Ç°° 4^.aô .~ ~ .^ a w .Ç Q u ~ OH _d

^_

iA

~

,~ u

~u ô_ ~ Ça

m

ô a â~ Ç = h~

â

u

.â X

ô 0 â ~ O a :y uC .C h L .

L .L.

N

C

h

O ~9

tio II $, o fi o

144

J. UEGAKI AND K. SHODA

The differential cross sections of the (e, e'p) reaction at B = 125 .3° for each element were obtained by integrating the (e, e'p) proton spectra in the region of the proton energy Ep z 5.0 MeV. The results are shown in figs. 2 and 3. The cross sections show IAR at E~ = 16.2f0.1 MeV m ia9La and at E~ = 15.0±0.1 MeV in t41 Pr, as discussed in the next section.

Fig. 4. The proton spectra of the "'Pr(e, e'p) reactions for B = 125.3°.

For the measurement of proton spectra, bombarding energies were selected at = 16.3, 15.5, 14.8 and 14.1 MeV on '4tPr, and at E~ = 17.1, 16.2 and 15.3 MeV on ta9La. Several targets with thicknesses from 13 to 15 mg/cmZ were used, except for the measurements at E~ = 16.3 MeV on 1`1Pr for which the target thickness was reduced to 8.4 mg/cmZ for higher resolution. Results are shown in figs . 4 and 5. E~

3. Analysis of the results 3.1 . THE RESONANCE IN THE (e, e'p) CROSS SECTION

The cross section for the (e, e'p) reaction can be expressed in virtual photon

i3~

20 16

~I~pr~e~ e,p)

145

. r10nm~/WV"rr '

t6 14 12 10 ~8 ~6 v ,~ 4 2 0 2 0 2 0

2

4

6

Fg . S. The proton spectra of the

8 ~

12 10 Ep (MeV)

39 La(e, e'p) reactions for B = 125.3°.

theory to) ~ ~ ~(e.e~p)(Ee) _ ~~ Qcr.v)("~N(Ee' ~E~

(2)

where dQ(r . pl(E)/dl~ is the differential photoproton cross section and N(Ee, E) is the virtual photon spectrum associated with an incident electron with kinetic energy E~. The photoproton cross section in the region around the ground IAS has two components : the T~ continuous part of the GDR, ~(â.pt(E), and the resonant part of the IAR, dt(Y, pl(E). Interference between the GDR and the IAS is included to ~(r. Pt(E). Using the component cross sections, eq. (2) can be written as ~ ~(a.e~Pl(Ee) - ~ ~i .vl(~N(E~' E)dE+ ~~ ~r.r)(~N(E~' Ek1E. J When a sharp strong resonance exists at ER, a sudden increase in dQ(e, ~,pt(E~)/dß should appear at E~ = ER based on a discrete photon spectrum at the endpoint energy of the virtual photon spectra for the second term of eq. (3). Such an increase was found at E~ x 16.2 MeV in the " 9La(e, e'p) cross section and at Ee .. 15.0 MeV in the "'Pr(e, e'p) cross section. In order to define the energy of the sudden increase, we calculated the diflference

146

J . UEGAKI AND K . SHODA

ui P ~

.

r Z a r

m b

f

d

ta

ce

n

acwwv)

~s

u

ts

te

E~cM.w

Fig . 6. (a) Difference between the " 9La(e, e'p) cross section and dash~ot line in fig. 2, which shows the position of the sudden increment from the f~~= IAR . (b) Difference betwcen the '"Pr(e, e'p) cross section and dash-dbt line in fig. 3, which shows the position of the sudden increment from the f,~Z IAR .

between the experimental (e, e'p) cross sections and a straight line approximating the (e, e'p) cross sections for energies below the sudden increase. This is shown by the dash-dot line in figs . 2 and 3. T'he results are illustrated in fig. 6. It is clear that the position ofthe sudden increase corresponds to the IAR found at E~ = 16.2±0.1 MeV for t 39 La and at E~ = 15.0±0.1 MeV for tat Pr . Since the first term of eq. (3) increases smoothly with energy, this part can be approximated by a quadratic function. If doRr,p~/dl2 is approximated by the BreitWigner shape, eq. (3) can be written as z ( ~ N(E~, EbE, ~ ~t~, .'P)(E~) = AE~ +BE~+C+D E +(Z~z J (E-

where !' is the resonance width, and A, B, C and D are parameters . Using T = 70 keV [refs. tt .tz)], the virtual photon spectrum obtained with DWBA calculations t 3 " ta) and correcting for the energy spread of the incident electrons, the method of leastsquare fitting is applied to the (e, e'p) cross sections in order to estimate A, B, C, D and ER. Results of the fit are shown in figs . 2 and 3 by the solid curves. The dashed lines show the first three terms of eq. (3), AE~ + BE~ + C. The parameter ER is found to be 16.2 f0.1 MeV for t 39 La and 15.0±0.1 MeV for l a ter. Integrated cross sections at the resonance can be obtained by using = ir(l'D. J ~ ~(r. pl(~E

(5)

ia9~ i~ipr(e

147

e~P)

Angular distributions of protons emitted through the E1 IAR can be represented by

2(cos B),

(6)

I(B) = a + 6P

where P 2 (cos B) is a spherical Legendre polynomial . Cross sections can be obtained from the differential cross section at 8 = 125.3°, for which P 2 = 0, as follows : °car . Pl(E~E = 4n ~ ~d~ ~r . pl(E~E~- 125 .3" J Cross sections are corrected for interference effects between the IAS and the GDR in the same way as in the previous paper 2); specifically

P1 dE = R a(ar .PFdE, J

_ ~I'rASQÇUp

(EIAR)

(8)

cos2 (~we -~cuß) I I ~~~ P1dE~

(10)

Q°naP~Q° near El,~, where Qçup (E,,Ue) is calculated from Qç ~F (E ~) and the ratio ~1 which are obtained from the (e, e'p) proton spectra and shown later (see figs . 7-10).

3 .2. IAR IN THE (y, pu) CROSS SECTION

Cross sections for the (y, po) reaction can be deduced from proton spectra from the (e, e'pa) reaction, which is described by d2 d = N(E~,E) (11) ~cr.Po)(`,, dIa dLadE P ~c~ .~->~1(E~,Ep) A E = EP A _ 1

+ SPA

where A and SP are the mass number and proton separation energy of the target N

Eu

2

Ft3 ô K1

a v b

v

0

'11FF  }~FFFII'FIFFFF~ 14

15

Ex (MeV)

IFFIIIIF'Fi

16

~B. 7 . The 139L8(Ys PO) Ci098 SCCtIOII.

17

148

l. UEGAKI AND K. SHODA

a s

!~u y0 ie

~Pr( Y,po ) A =125 .3°

s

a4

~i ffff}~

b 3

#;

z F;,, i,~,*~ 0

m

t ~a

u

Ex (MeV)

Fig. 8. The ' 4' Pr(y, Po) aces section.

nucleus, respectively . Since the energies of the first excited states of the residual nuclei isaga and' 4 °Ce are E,~ = 1.4 and 1 .6 MeV, respectively, the proton spectra in the uppermost region of 1.4 MeV for t 39 La and 1 .6 MeV for 1 ~tPr relate to po only. Using eq. (11~ (y, po) differential cross sections were obtained from the spectra in these energy regions. The results are shown in figs. 7 and 8 and the integrated cross sections for the IAS are also shown in table 1. Tea~e 1 Strength of the resonance in the (y, po) and (y, p) reactions on ' 39 La and "'Pr, and the ratio of proton group 1 and proton group 2 emittod through the E,~= IAR Jai;!p°~dE (pb ~ MeV)

Ja~~~dE (pb ~ MeV)

Proton group 1 (~)

Proton group 2 (~)

44 f9 <5

240 t30 260f30

40 f 10 Sf S

60 t 10 95 t S

3.3 . PROTON SPECTRA EMTIT$D THROUGH THE IAR

Proton spectra from the (e, e'p) reaction consist of various proton groups (ps) corresponding to the residual states z. Spectra, Y(E~, E~ can be expressed as

(12)

1~9i e

9

70 11

12

13

14 15 16 17 hv tMev)

Fig. 9. (a) The photoproton spectrum emitted from the on-resonance region on '"Pr corresponding to the virtual photon whose spectrum is shown by the solid curve in (c). (b),The photoproton spectrum emitted from the off-resonance region on "'pl. corresponding to the virtual photon whose spectrum is shown by the dashed curve in (c). (c) The virtual photon spectra givrn in eq . (15). The solid and dashed curves wrre spond to (a) and (b), respectively . Arrow shows the position of the f,~i IAS.

141p~e'

e~p)

149

Fig. 10 . The photoproton spectrum of "'La . The caption is the same as for fig. 9.

I50

J. UEGAKI AND K. SHODA

where the proton energy EP= is related to the excitation energy E and residual energy Ex by

A linear combination of the proton spectra of two bombarding energies, as described by Y(E~ t, E~ 2, E~ = Y(E~ t, Ev)-kY(E~ 2, E~ = N*(~~ dtà ~tr. pxl(~

,

N*(E) = N(E~ 1 , E)-kN(E~~, E),

(14) (15)

shows a proton spectrum obtained from a photon spectrum of N*(E) which can be approximated by a moncenergetic virtual photon spectrum peaked at E~ Z with choice ~of a suitable coefficient k (the photon-difference method). The results of Y(E~ 1, Eat , E~ and the corresponding virtual photon spectra N*(E) for ' 39 La and 'a'Pr are shown in figs . 9 and 10. Because the f~ IAR was found at ER = 16.2 MeV for ' 39 1:.a and at ER = 14.9 MeV for ' a' hr, figs . 9a and l0a are the spectra including the IAR and figs. 9b and lOb are the ofl~resonance spectra. The former consists of

ao

0

Fig. 11 . (a) The energy distribution of protons emitted through the f., r~ IAR in "'pi. . (b) The decay mode of the f,~= IAS given by the proton scattering experiment '°) .

Fg . 12 . (a) The energy distribution of protons emitted through the f= IAR in "9La. (b) The decay mode of the f,~2 IAS given by the proton scattering experiment '6).

~a9~ . mp~~~.

I51

~~F)

the protons emitted through the IAR and the continuously excited states in the GDR. The latter consists of protons emitted only through the continuously excited state . The virtual photon spectra, shown in figs. 9c and lOc, have approximately the same shape after shifting the photon energy . Also it can be assumed that the configuration of the excited states as well as the cross section in the continuous part are approximately constant in the region of 900 keV for' 39 La and 700 keV for "'Pr . Then the energy distributions of protons emitted through the IAR can be approximately' obtained by means of subtracting the off-resonance spectra from the onresonance ones after shifting the former to the high energy side by 900 keV for 139 and 700 keV for i 4 'Pr. The results are shown in figs . l la and 12a. The absolute values are indicated by the cross sections, after dividing the proton spectra by the virtual photon number at the resonance energy, which leads to ~r.v~l (EP,4A 1 +S P +E s 1 .

(16)

Each term in eq. (16) shows the component of the resonance cross sections for the (y, pr) reaction corresponding to the position of the residual energies E,~ The data obtained from the proton scattering experiments'z~ is . ie) are shown in figs . llb and 12b, after modification with the present resolution of 200 keV, for ~ ~P .P=1

(17)

(Ev AA 1 +S P +E s l .

Eq. (17) is expected to be proportional to eq . (16) under the assumption of compound nucleus formation. Results for the two reactions do not correspond exactly with each other because of unequal interference effects. As the effects of interference between the IAS and the GDR are difficult to detenmine with the present experimental resolution, the results from the (e, e'p) reaction and the proton scattering in the figures are only normalized to the po group for'~'Pr. The' 39 La data were not normalized because the po group in the (e, e'p) result was absent . 3 .4. IAR ANALYZED FROM THE ISOCHROMAT

Isochromats are defined by the proton yields integrated in the fixed range of that is I(EC' Epl' - fEP= d dE (18) EPZ) °~ dEelp~ JEo~ P

EP , 5 EP 5 EPZ ;

It is expressed using the relation EP I(E~' EP1~ EPZ)

A -1

=

[(A -1)/A](E - S P - Ex) eP=+ so +E=

as follows

~ ~~r.Px~(E)N(E~, E)dE, A -~ x E~,+S o +Ex A ,A = = Evl Evl A-1 ~ EPZ EPZ A-1 . =

(19)

152

J. UEGAKI AND K . SHODA

The factor (A-1)/A in eq. (19) can safely be approximated by 1 for the present nuclei. The aim of the analysis is to determine whether a sharp resonance exists for the proton channel feeding to the special residual states found in the proton spectra (figs. 11 and 12). The cross section Q(r. Pxl(E) can be divided , into two parts as ~(Y. Px)`E) -

12~)

Q Y . Pxl(a.l+~'. px)`E)~

where Qr . Pxi(E) and aRY, Pxl(E) are the continuous and IAR components of the cross section, respectively . The second part of eq . (20) contributes only near the resonant energy so that the proton groups emitted through resonance feeding to the various residual states x contribute to the isochromat only near the resonant energy. On the other hand, the first part of eq. (20) contributes to the isochromat in a broad continuous region, so that the isochromats appear continuous if the contributing residual states overlap. But if the reactions through the continuous states leave a well separated single group of the residual states at EF and also if the reactions through IAR leave the residual states at Ex", then eq. (18) can be expressed as I(Ee, EP 1+ EP 2)

-

f

EPi+SP +E x

C %~ ~(r.Pxl`-'N(Ee~ E E

J E~, + SP + E,e

+~ s'

('EP = +SP+Ex " EP,+SPtEx"

~,,.Px,~(E)N(E~, EbE.

(21)

Since N(E~, E) vanishes for E > E~, the first term of eq . (21) can contribute only when E~ is larger than the lower limit of the region of the integration, that is The second term of eq . (21) contributes only in the region of E'é =- EP,+SP +Ex" 5 ER 5 EP 2 +S P +E,~

if the resonance width is narrow enough, and it is proportional to the resonance strength . In order to discuss dl(E'~, dE~), the increment of the isochromat between E~ and E~+dEe, ~r.Pl(E) is assumed to be constant in the integration region dEe, where dE~ is smaller than dEP = EP2 -EP, . In this case, because of the relations ~+dEP

('E~ + dEP

JE6

~c. Pxl(~N(E~ + dE~, EbE E~+dE. -

J Er, ~

E~+dEP

E~, EbE + ~ °(r. Px)`~N(~ + d

E~+dE.

,.(~ /~EL+dE.

Q;.Pxl(E)N(Eé + dEQ, EbE

ta9~, tupr~e~ ép)

n

O

0

y

V b 0

o

V a W V

a0

3

0 u

0

k

b

C O q

d

4 V a W V

Cw ~° ~~

d a

N `r

Ô~ .~ Ô .. ~ F o m W y~ h

Ir 4~ i a+

V

Ô

t el Va W V a

~,~ b

r

~7

30

k w

v a

G

V~

~â

~

-y +

:p

", O V W V r

.. .

r~

N

v

~ àô 4 Ô .Çq G. u

v u

an u .d

1..Ô

u O É

m

4.r

O

ÇL u aï

.a

O h ~~s~=w~~Olx) I

a

R n

30

a W

tV

Ô Ô

0 s

4 O V

a

~r

W Ô .

1

153

w

a

OW r Va W V

w o

m

.. Ô

~ ~s~=w~ ~~Olx ) I

â

eb

J. UEGAKI AND K. SHODA

where E~ 5 E~ 5 E~ + d E~ and second term of middle formula has vanished, the increment can~be expressed as dl(E'~, dE~) = 1(E~+dE~, Epl , Ep2)-I(E~, Epl , Ep2) p,~~(~)

~

E{+dE

E6

+~ x

e

N(E~+dE~, E~E

('E~ + dE . Et~

~~ .pxi(E)[N(Eé+dE~, E)-N(E~, E)]dE.

(23)

The sum in eq. (23) is taken over the residual state x' in the region ER -S p -Ep l z E~, z ER -Sp -Ep2.

(24)

The same relations hold for the differential cross section. Because the residual ground states of the 139 1.a(e, e'p) and 141Pr(e, e'p) reactions are isolated from the other residual excited states with an energy larger than about 1 .4 MeV, the method mentioned above can be applied as follows. Isochromats have been obtained from the ' 39 La, ' 41 Pr(e, e'p) differential cross section data with proton energy width dEp x 0.6 MeV and proton energy steps of 70 keV. Examples of the isochromat of the 141Pr(e, e'p) reaction are shown for the po region in fig. 13, in which the increase due to the first term of eq . (23) is shown by the solid arrow. The position of this increase was compared with E~ calculated by eq. (22) and a small shift was found so that the position can be expressed by El~ + dE~ . The shift energy dEl~ may arise from errors in the electron and proton energies, or from the fact that the value of the integration in eq . (19) near E~ = E~ is small. The estimate of dEl~ (= 200 keV) obtained for the po group of 141Pr is applied to other analyses of isochromats. In the case of l a 9 I-a, the residual excited states for the ot3resonance part may not be a single level but they seem to concentrate in a narrow energy region as shown in fig. 10. Corresponding to this, the same kind of increase in the isochromats as in the case of the po group in 141 Pr is found, as shown in fig. 14. Similary, based on the proton spectra for 141Pr shown in fig. 9, the residual states for the otiresonance part of this nucleus seem to concentrate into an excited state in addition to the ground state. Since both groups are well separated, a similar treatment as in the case of 1391.a is applied to the p' region for 141Pr. After the correction for the energy shift dE~, a quantity ô(El~ + d E~) is defined using eq. (23) as follows : d(Ele +dE'e) J

d1(Ele +dE'~, dE~) ~+eEL N(Ele +dEle +dEe, EbE

(25)

139~

141p,.~e

155

e~P)

z ~(r.vxl(~e+dE~) Et'+eE6+eE,

E6 + x" +eEt

(26)

/'E~ t dE`

N(E~+dE~+dE~, E~E

E6

In order to calculate Q(E~+dE~) from the isochromats, a linear function Y(E~, E~+dE~) is defined for an approximation to the isochromats I(E~, Ept , Ep2) in the range E~+dE(~-dE~ 5 E~ 5 E~+dE~+dE~ as Y(E~, E~+dE~) = AE~+B+kC(E~-E(~-dE(~), where k1=

(0,

(27)

for E~ 5 E~ + dE~

1,

for E~ > E~+dE~,

,s.~ .

tb so

v'

40 40

~~~~~~i,i,ip'~°~~~III~~

20

ii~h 0

uip,

Db

(b) .

tb 4c

20

0 L 14

~II

il

15

I

tb 10

II

~E

16 E (M.V)

i~iiii,iupi~ip

5

0

~I 15

16

7

E(MW)

Fig . 15 . The result of eq . (25) calculated from the isochromats, where Er=E~+dE~+ ;d E, (sce sub and (d) Po group in 139 . sect . 3.4). (a) p' group in 141 Pr . (b) P o group in 141pr . (c) P~ group in 139

156

J. UEGAKI AND K . SHODA

and A, B and C are parameters . The parameters are obtained by least-square fits to each isochromat. The most probable value of C is used to estimate the quantity dl as dl(E'e +dE'e, dEQ) = CdE e,

(28)

where dE~ = 200 keV and dEe = 400 keV were applied. Using this estimate, ô{E~+dEe) is obtained from the definition in eq . (25). Actual calculations were performed for the differential cross section, and the results are shown in fig. 15. The numerator of the second term in eq. (26) is zero everywhere except near the resonance. When the energy E~ is taken to be equal to E'é, corresponding to the resonance energy, the numerator mentioned above can be approximately reduced to ~+es;+ee, (29) .px~l(~N(~e+dE'~+dE~, EbE, . ~cr J ~+eue x which is obtained by a similar calculation for eq. (23). The value of eq. (29) has a maximum at E~+dE~ x ER if T ~ dE~, and the maximum for Ex -ZdE< < E~+dE'< < ER

if l' x

dE~.

The denominator of the second term in eq . (26) is approximately constant because of the similar photon spectrum. In fig. 15, the energy scale is given by so that the second term of eq. (26) takes a maximum value at E = Ex ± 4d E~. Because the first term of eq. (26) changes slowly with energy, the structure shown in fig. 15 suggests the existence of strong narrow resonances at E = ER±4dEa. 4. Discussion of the results The ground f~ IAR can be seen clearly in the '41Pr(y, po) differential cross section (fig. 8). The estimated energy and strength of this IAR are 14.8 f 0.1 MeV and 3.5 ±0.7 ~b " MeV/sr, respectively . These values are consistent with the resonance energy of 14.9 MeV given by other experiments' 1" ' s.l'.ls) and the theoretical estimate, and also with the resonance strength obtained by the (p, yo) reaction "). The dit%rential cross sections for 139La(y, po) (fig. 7) do not clearly show the f~ IAR and the strength is estimated to be less than 0.4 deb " MeV/sr at the position of the f~, IAR. In the dif%rential cross sections of 1391:,a(e, e'p) shown in fig. 2, the f~, IAR is clearly seen and its energy and strength are deducedas 16.2 ±0.1 MeV and 21 f3 pb ' MeV/sr, respectively . This resonance energy is consistent with those given by other experiments ~s, ie . i9. so) and the theoretical value of about 16.2 MeV. The îs91-,a(y, po) results and the 139La(e, e'p) diûerential cross sections suggest that almost all proton decay branches through the f.~ IAR in is9La consist of the channels feeding to the

ts9~~ tatß.(e~ e'P)

157

excited residual states. The resonance strength deduced from the t 39La(e, e'p) result is not consistent with the ß~ecay result') and theory 2 _ s). The differential cross sections for ' 4' Pr(e, e'p) do not show as large a change due to the f.~ IAR as was apparent In "9La; this smaller incremental ef%ct is due to the large non-resonant contributions from the T~ states of '4 tPr . However, from the results shown in fig. 6 and the t4tPr(y, Po) ~~~ ~ fi& 8, it is clear that the energy of the f~ IAR is 15.0 f0.1 MeV in the "' Pr(e, e'p) differential cross section. This energy is consistent with other experimental results t'. t'). The 0.2 MeV difference of the f~ IAR energy between the results of tat Pz{Y, po) and of t~tPr(e, e'p) may be caused by the errors in the absolute values of the proton and electron energies. The IAR in the (e, e'p) reaction for '39La and t"Pr were studied in the previous paper s~ and the present results have been determined by an independent series of experiments. Table 2 compares the various results. T~at.e 2 Comparison of the experimental results of the f,~= IAR m ` s9 l,a and ta`pl, Element Realion tatpr

139

Es (MeV)

(P. Yo) (p, po) (p, p') (e, e'p) (e, e'p) (e,e'po)

14 .95 f 0 .05 14 .918 f 0 .01 14 .92 f 0 .01 14 .9 1 S .0 t 0.1 14.8 t0.1

Po) (p, p') (e, e'p) (e, e'p)

16 .17 16 .16 16 .1 16 .2 f 0 .1

(P .

(~" e~Po)

fa`, . ~ tdE Jat~tdE fd~`~. PtdE Jat~tdE (pb~MeV)~(pb~MeV)(pb~MeV) (Pb~MeV) 112 f 11

104t21

< 12

44f9

< S

770 t 250 411 t 3

Ref tt ) m) t ~)

57 t 22 630 t 100 442 t 3

rw

(eV)

300 f 40 240 f 30

520 t 180 260 t 30

15 f 2 s) (24 f 3)') present work 10 .2 f 2 .1 present work z~ i6)

35 t 12 s) (35 t4)') present work < 1 .3 present work

') This shows a wrong value because it is calculated from the total photoproton cross section which contains not only proton group 1 but also proton group 2 . See text.

The decay branches through the f~ IAR in t "Pr(e, e'p) and t '9lra(e, e'p) were given in figs . 11 and 12, respectively . In the case of4tPr, two different proton groups are found in fig. 11. One of these proton groups agrees with the proton scattering results, but the other proton group feeding to arôund the 2 MeV residual states does not correspond to the proton scattering result as shown in fig. 11. Hereafter the former and latter groups are denoted as proton group 1 and proton group 2, respectively . The proton group 1 consists of; in addition to those feeding the ground state, the neutron particle-hole states in the residual nucleus which are characteristic of the f~ IAS confïguration. The proton group feeding the particle-hole states is not clear with the present statistical error but the po group is distinct . Comparison in the

158

J . UEGAKI AND K . SHODA

figure shows that the proton group 1 is emitted from the f; IAS. Proton group 2 corresponds to residual states in the region 2.0 < Ex < 2.8 MeV. The protons of this group seem to be emitted through the IAR in the (e, e'p) reaction with a different mode from the resonance, which may be characteristic of the electromagnetic excitation. In the case of ' 39 La, the protons emitted through the resonance at the f, IAS consist only of proton group 2, as shown in fig. 12. Proton group 1 does not have a noticeable strength in this case. This means that the yield of the proton group emitted with the decay mode of the f~ IAS in ' 39La is negligible, which is consistent with a small ß~ecay matrix element between the corresponding states. Almost all the strength of the f~ IAR in ' 39 La(e, e'p) is due to proton group 2. Similar to the case of iaipL, this proton group 2 does not seem to relate to the configuration of the f~ IAS. However it is now an open problem why the dominant proton group 2 is emitted through such a sharp resonance at the position of the f~ IAS, as shown by the sudden increase in the (e, e'p) cross section. Further evidence to support the above result is shown in fig. 15. For 'a' Pr, the resonance is at 15.0±0 .1 MeV for proton group 1, as shown in fig. 15b, and also at 15.2 f0.1 MeV for proton group 2, as shown in fig. 15a. In the case of ' 39La, the resonance for proton group 2 is found at 16.2 f 0.1 MeV,. as shown in fig. 15c. In fig. 15d, the resonance is not clear for proton group 1 in ' 39La. A slight energy shift was found between the resonance for proton groups 1 and 2 for 1 ~ 1Pr as shown in figs. 15a and b. This seems to show a possibility for the IAR to appear at a diRerent energy around the position of the IAS depending on the emission mode. This shift of the resonance does not contradict the shape of the iaipr(e, e'p) cross section, which shows a rather gradual increase around the IAR compared to the 139 La(e, e'p) case, as shown in figs . 2 and 3. This suggests a separation of the resonance. However definite confirmation of this result needs more precise eaiperimental studies. The resonance strength can be approximately estimated from the results in fig. 15. Under the approximation that the first term of eq. (26) is constant, the second term can be estimated from the value of Q-QC at the peak of the resonance. After slightly modifying eq. (26), the strength can be obtained as follows : /'ER +~dE,

ER-}dE, z

~(r .n=~(~N(ER+âdE~, ~E ER+~dE,

x N(ER + 4dE~, ER ) ~ ~ x

ER-}dE,

~cr . r=1(~E+

(31)

where the integration may cover almost the whole resonance region and the range of the summation for the residual states is limited by eq . (24). Results of this estimate are shown in table 3, accompanied by results calculated from the decay proton spectra in figs . 11 and 12. Both results are consistent with each other.

139~ 1 " 1~(e~ e.p)

159

TABLE 3 from Partial strength of the f.,~ z IARcalculated the isochromata and the spectrum in the (e, e'p) reaction

Integrated cross section (pb ~ MeV/sr)

Energy of residual state (MeV) lal~

141~ 139~

The relation

0

1 .2
~PI (EkiE _ (~~)z

2J 2J

from isochromata

from spectra

llt 2 21t10 9t 5

lOfl 13f3 7t2

+ l r rr +1 r

(32)

can be used to calculate the radiative width from our experiment, where J t,,,s, J~, rP and rY are the spin of the IAS, the spin of the target nucleus, the proton width which corresponds to ~~~ pr and the radiative width of the IAS, respectively . For this relation we should use d~Pl and rp related only to.po or proton group 1. The radiative widths calculated using the pa strength are shown in table 2. In a previous paper 3), the radiative width was calculated using ~~I which contains not only proton group 1 but also proton group 2. Fïirther, the assumption ~~c,~r = 1 was also used. For the f~ IAR in iaiPr, the errors from these two assumptions cancelled each other and therefore the previous value of rY was nearly equal to the present value. Actually the ratio ~rp~r x Z is known from proton scattering t °) for this IAS. For the f~ IAR m t 39La, the present value for the radiative width is very small and is consistent with the ß~iecay experiment'). S. Conclusion The f~ ,ground IAR in t 39La and tatpr induced by electromagnetic excitation decays by two proton channels. One of them shows the reaction mode reflecting the corresponding IAS. The other does not correspond to the configuration of the IAS but is caused by some other process. In the case of'a'Pr, the strengths of the two processes are nearly equal, but in the case of 139La the decay channel of the f~ IAR is mainly the latter process. The latter type of channel appears in the IAR in both nuclei and is not found in proton scattering . This suggests that it is a special mode in the electromagnetic interaction with the IAR. However, precise explanations cannot be given. The latter process is the cause of the enhancement of the transition strength of the spin-flip f~ IAS which disagrees with the results from the (p, yo) and ß~ecay experiments as well as with theory. The correction for this process must be made in order to extract the electromagnetic strength for the IAS, particularly for the spin-flip type in which the strength is very small.

160

J. UEGAKI AND K. SHODA

More detailed study is needed to elucidate the reaction mechanism of these resonances and may provide important information for phôtonuclear reaction mechanisms . The authors would like to thank the machine group and the computer group in the laboratory for their help in the operation of the linear accelerator and the computer. They are also very grateful to Drs. M. Sugawara and T. Saito for their useful discussions and amiable help. References 1) J. I. Fujita, Phys . Lett . 24B (1967) 123 2) K. Shoda, A. Suzuki, M. Sugawara, T. Salto, H. Miyase and S. Oikawa, Phys . Rev. C3 (1971) 1999 3) K. Shoda, A. Suzuki, M. Sugawara, T. Salto, H. Miyase, S. Oikawa and B. N. Sung, Phys . Rev. C3 (1971)2006 4) Y. Tanaka and K. Ikeda, Prog . Theor. Phys. ~ (1972) 840 5) T. Terasawa and J. Fujita, Nucl . Phys . A223 (1974) 492 6) K. A. Snover, J. F. Amann, W. Hcring and P. Paul, Phys. Lett. 37B (1971) 29 7) L. Szybisz, F. Krmpotic and M. A. Fariolli, Phys. Rev. C9 (1974) 624 8) C. P. Browne and W. W. Buechner, Rev. Sci. Instr. 27 (1956) 899 9) K. Shoda, M. Sugawara, T. Salto and H. Miyase, Nucl. Phys . A221 (1974) 125 10) R. H. Dalitz and D. R. Yennie, Phys . Rev. 106 (1957) 1598 I1) H. Ejiri, P. Richard, S. Ferguson, R. HefFner and D. Perry, Nucl . Phys . A128 (1969) 388 12) H. Seitz, D. Riak, P. von Brentano, J. P. Wurm and S. A. A. Zaidi, Nucl . Phys. A140 (1970) 673 13) E. Wolynec, G. Moscati, J. R. Moreira, O. D. Goncalves and N. N. Martins, Phys. Rev. Cll (1975)1083 14) W. W. Gargaro and D. S. Onley, Phys . Rev. C4 (1971) 1032 15) J. P. Wurm, A. Heusler and P. von Brentano, Nucl . Phys. A128 (1969) 433 16) G. C. Morrison, N. Williams, J. A. Nolen, Jr. and D. von Ehrenstein, Phys. Rev. Lett . 19 (1967) 592 17) N. Marquardt, P. Rauser, P. von Brentano, J. P. Wurm and S. A. A. Zaidi, Nucl . Phys. A171(1971) 33 18) A. Heusler, H. L. Harney and J. P. Wurm, Nucl . Phys . A136 (1969) 591 19) C. A. Wiedner, A. Hewler, J. Solf and J. P. Wwm, Nucl . Phys . A103 (1967) 433 20) L. Veeser and W. Haeberli, Nucl . Phys . A116 (1968) 172