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Coherence effects in the (p, α) reaction
Volume 53B, number 4
PHYSICS LETTERS
23 December 1974
C O H E R E N C E E F F E C T S I N T H E (p, a ) R E A C T I O N J.W. SMITS, F. IACHELLO, R.H. SIEMSSEN and A. Van der WOUDE
Kernfysiseh VersnellerInstituut, Groningen, The Netherlands Received 5 November 1974 Coherence effects between the picked-up proton and di-neutron configurations are shown to dominate the (p, a) reaction in agreement with a model proposed by Bayman. An approach based on the separation of the di-neutron and proton excitations yields a quantitative description of the relative population of states m the I tSSn (p, a)l 1Sin reaction.
As a direct process the (p, a) reaction proceeds via the pick-up of two neutrons and a proton. Starting with a spin-zero target the reaction can coherently excite configurations where the proton hole is coupled to the ground state as well as to those states in the (Z, N - 2 ) nucleus which are strongly excited in the (p, t) reaction. Although the theory of the (p, or) reaction was formulated more than a decade ago [ 1], studies to this date have concentrated on the dynamics of this process and have neglected detailed structure effects. Somewhat more quantitative analyses have been based on the "spectator model" in which the removed neutrons are assumed to form a spin-zero coupled pair with zero orbital angular momentum and in which therefore coherence effects resuiting from neutron excitations are ignored [2]. In the spectator model only those states will be populated which are also seen in one proton pick-up reactions leading to the same final nucleus. To study coherence effects in the (p, ct) process we investigated the 118Sn(p ' a)115 In reaction. The choice of target was prompted by the fact that (i) the tin nuclei have a closed (Z= 50) proton shell and (ii) the neutrons are in a superconducting state. The proton shell closure leads to a simple proton-hole spectrum in 115 In while the superconducting neutron leads to a concentration of the strength of the neutron excitations in a few states. In fact in the 118 Sn(p, t) 116 Sn reaction most of the pair strength is concentrated in the 0 + ground state and the 2 + first excited state [3]. Moreover, the low-lying states of 115in are well described in the framework of the weakcoupling model in which the proton holes are coupled to the vibrational excitations of 116Sn" Carbon-backed tin targets of ~ 150 tag/cm2 thickness were bombarded with 22 MeV energy analysed protons from the K.V.I. cyclotron. Alpha-particles were detected in an array of four stopping detectors which were followed by veto-detectors to gate out the long-range particles. The total energy resolution was ~ 35 keV. The peak fitting program AUTOFIT [4] was employed to analyze the spectra. Angular distributions of states up to ~ 1.5 MeV excitation are shown in fig. 1. The spin assignments are based on previous work as summarized in refs. [5, 6]. In addition to the proton-hole states seen in the (d, r) reaction [6] and expected on the basis of the "spectator model" other states are observed, as will be discussed further on. Also the relative intensities of the states populated in the (p, a) reaction differ from those in the (d, r) reaction. These facts already indicate that a simple spectator model fails to explain the present data. The curves in fig. 1 have been calculated with the DWBA code DWUCK [7] with a triton cluster form factor and with the optical model parameters of refs. [8, 9]. The parameters for the triton cluster were r o = 1.25 fm and diffuseness a = 0.45 fm. Noteworthy is the small value needed for this diffuseness parameter to obtain good fits to the data. A spin-orbit interaction was only included in the proton channel. Generalising the expression of Bayman [1 ] to the case where the protons and neutrons are occupying different shells one obtains for the cross section of the (p, a) reaction
~-~)
x
= D'[~-~)DWBA" lp,l\AZ"3]
o o; *np p
Op) 0
"~--~]
" I / ' ( 2 ] p + ~ I + 1)
0
.
z
2
[ •
(1)
337
Volume 53B, number 4
PHYSICS LETTERS
23 D e c e m b e r 1974
KVI 629 10 3
--
I0 2
_
I02
102 ~ , ~
000
~
9/2*
104
129 13/2 ÷
s12-
IOI
•
i0 - ' .~ t c~ i0 I
'~ ¢•
- ' ~
0 34 I/2 -
'T~,) ,If' 1085/2+
i0~
I 45 9/2+
10¢
~
b "Io
0 60 3/2_ I0 F
I0
i0 ) _
I 14 11/2+
00
I 30
I 60
io2_
101
't ! 0
I 30
I 60
149 9/2+
_ 0
I
50
l
60
OCM Fig. 1. A n g u l a r d i s t n b u t m n s o f s t a t e s e x c a t e d in t h e l l S S n ( p , a ) l l S l n r e a c t i o n at E p = 22 MeV. T h e c u r v e s are t h e r e s u l t s o f DWBA c a l c u l a t i o n s .
Here it is assumed that the DWBA cross section does not depend on the microscopic neutron and proton configuranons; D is an overall normalisation factor which is the only free parameter. The first two terms in eq. (1) are center-of-mass corrections and the term x/(2J+ 1)/(2ip+ 1)(21+ 1) is the ratio of the three to the two partial fractional parentage coefficients. The Moshinsky bracket transforms the di-neutron with orbital angular momentum L = I and radial quantum number N and the proton to a triton with quantum numbers of c.m. motion N, L. The last bracket performs the. transformation from j/to LS .coupling. The coefficients O/L~ ~7l are the weak-coupling . . . . lp) amphtudes for coupling the proton hole lr(jp 1) to the neutron excitations of spin I to form a final state with spin J. A calculation coupling the 099/2, lpl/2, lP3/2,0t"5/2 and 0f7/2 proton holes to the zero-, one- and twophonon quadrupole and octupole vibrational states was performed to obtain the cVL~ ~71;~ . J p . is the proton • . . Jp' spectroscopic amplitude (x/~/p = ~ and the dl-neutron spectroscopic amplitude ~ is given by
:
)
× (11 ~ (il)12 } U2);lltl
12 (/)} ~ ( 0 ) ; I ) ' ( ~ 1 0 0 ;1In 1 l I n 2 12;D.
(2)
It already contains the coherence of the di-neutron configurations and can be obtained from (p, t) data through a 338
Volume 53B, number 4
PHYSICS LE'Iq'ERS
23 December 1974
KVI 575
X2
118Sn (P,Ot)il51n
13/;~ II/~ ~f/Z-
Zt/i
i/2-
9/~
50
?__. z5
0
i
-i
I,,,-
=: 25
1'4
'~ ,'2
I'o
e
~
'
b
o
EXCITATION ENERGY (llleV)
Fig. 2. Strengths of the liSSn(p, a)llSln reactmn for different signs of the relative phase of the two neutron amplitudes. The same normalisation constant was used in both eases. DWBA calculation with a cluster formfactor. For this the DX optical model parameters of ref. [3] were used. The importance of eq. (1) is that it separates proton and neutron excitations by assuming that the respective amplitudes can be independently determined. In the present case the 0 + ground state and the 2 + vibrational state dominate in the weak-coupling wave functions and the Ix/~-2÷/V~0÷I ratio was determined from a fit to the data of Fleming et al. to lie between 0.5 and 0.6. In fig. 2 the predicted (p, or) strengths (open bars) are compared with those obtained from experiment. For positive sign of the Ix/~2./x~0+l ratio (only the absolute ratio can be determined from the (p, t) experiment) there is a remarkable agreement in the relative intensities. Of special interest is the 5•2- state at 1.04 MeV which is very strongly seen in the (p, t~) reaction in agreement with theory and which in contrast is only weakly excited in the 116Sn(d ' r)115 In reaction [6]. From the calculations it follows that this state has a strong Ipi-/1 ® 2+> component. Also the ratio of the 9•2 + g.s. to the 9•2 + excited-state strength (for the 1.45 and 1.49 MeV states combined) is more than doubled compared to the (d, T) reaction due to constructive and destructive interference respectively by the Ig~/~ ® 2 +) component excited in the (p, a) reaction. Noteworthy are also the 11/2 + and 13/2 + states of the gg"f2® 2+ weak coupling quintuplet. Whereas the 13/2 + state is very strongly populated, the 11/2 + state is only weak in agreement with the theoretical predictions. The 7/2 + state has not been resolved, but the calculated number corresponds roughly to the upper limit for a possible state at 1.47 MeV in the (p, a) spectrum. To our knowledge the present analysis presents the first case in which the coherence properties of the (p, a) reaction properly have been taken into account. The striking agreement between the theoretical predictions and experiment demonstrates the usefulness of the (p, t~) reaction as a spectroscopic tool in particular for the study of weak-coupling configurations. From the cross-section ratios the relative phase of the two-neutron amplitudes can be experimentally determined. The help of Professor Arima in the derivation of the expressions for the (p, ~t) cross sections is gratefully acknowledged. We also thank Drs. W.H.A. Hesselink and S.Y. van der Werf for their assistance in the data taking. This work was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nededandse Organisatie voor Zuiver Wetenschappelijk Onderzoek" (ZWO).
339
Volume 53B, number 4
PHYSICS LETTERS
23 December 1974
References [1] B.F. Bayman, Nuclear spectroscopy with direct reactions, Vol. II, Argonne National Laboratory Report, ANL - 6878 (1964) p. 335; J.A. Nolen, Ph.D. thesis, Princeton 1965, unpublished. [2] W.R. Falk, Phys. Rev. C8 (1973) 1757, D.L. Dittmer and W.W. Daehnick, Phys. Rev. C2 (1970) 238; C. Glashausser, D L. Hendrie and E.A. McClatchie, Nucl. Phys. A222 (1974) 65; M. Vergnes, G. Rotbard, J. Kalifa and G. Berrier-Ronsin, Phys. Rev. C10 (1974) 1156. [3] D.G. Fleming, M. Blann, H.W. Fulbright and J.A. Robbins, Nucl. Phys. A151 (1970) 1. [4] P. Spmk and J.R. Erskine, Argonne National Laboratory Report ANL-PHY-1965B; J R. Comfort, Argonne Physics Division Informal Report, PHY-1970B [5] C.V. Weiffenbach and R. Tickle, Phys. Rev. C3 (1971) 1668. [6] W.H.A. Hesselink et al., Nucl. Phys. A226 (1974) 229. [7] P.D. Kunz, private commumcation. [8] C.M. Percy and F.G. Perey, Atomic Data and Nuclear Data Tables 13 (1974) 293. [91 L. McFadden and G.R. Satchler, Nucl. Phys. 84 (1966) 177.
340
PHYSICS LETTERS
23 December 1974
C O H E R E N C E E F F E C T S I N T H E (p, a ) R E A C T I O N J.W. SMITS, F. IACHELLO, R.H. SIEMSSEN and A. Van der WOUDE
Kernfysiseh VersnellerInstituut, Groningen, The Netherlands Received 5 November 1974 Coherence effects between the picked-up proton and di-neutron configurations are shown to dominate the (p, a) reaction in agreement with a model proposed by Bayman. An approach based on the separation of the di-neutron and proton excitations yields a quantitative description of the relative population of states m the I tSSn (p, a)l 1Sin reaction.
As a direct process the (p, a) reaction proceeds via the pick-up of two neutrons and a proton. Starting with a spin-zero target the reaction can coherently excite configurations where the proton hole is coupled to the ground state as well as to those states in the (Z, N - 2 ) nucleus which are strongly excited in the (p, t) reaction. Although the theory of the (p, or) reaction was formulated more than a decade ago [ 1], studies to this date have concentrated on the dynamics of this process and have neglected detailed structure effects. Somewhat more quantitative analyses have been based on the "spectator model" in which the removed neutrons are assumed to form a spin-zero coupled pair with zero orbital angular momentum and in which therefore coherence effects resuiting from neutron excitations are ignored [2]. In the spectator model only those states will be populated which are also seen in one proton pick-up reactions leading to the same final nucleus. To study coherence effects in the (p, ct) process we investigated the 118Sn(p ' a)115 In reaction. The choice of target was prompted by the fact that (i) the tin nuclei have a closed (Z= 50) proton shell and (ii) the neutrons are in a superconducting state. The proton shell closure leads to a simple proton-hole spectrum in 115 In while the superconducting neutron leads to a concentration of the strength of the neutron excitations in a few states. In fact in the 118 Sn(p, t) 116 Sn reaction most of the pair strength is concentrated in the 0 + ground state and the 2 + first excited state [3]. Moreover, the low-lying states of 115in are well described in the framework of the weakcoupling model in which the proton holes are coupled to the vibrational excitations of 116Sn" Carbon-backed tin targets of ~ 150 tag/cm2 thickness were bombarded with 22 MeV energy analysed protons from the K.V.I. cyclotron. Alpha-particles were detected in an array of four stopping detectors which were followed by veto-detectors to gate out the long-range particles. The total energy resolution was ~ 35 keV. The peak fitting program AUTOFIT [4] was employed to analyze the spectra. Angular distributions of states up to ~ 1.5 MeV excitation are shown in fig. 1. The spin assignments are based on previous work as summarized in refs. [5, 6]. In addition to the proton-hole states seen in the (d, r) reaction [6] and expected on the basis of the "spectator model" other states are observed, as will be discussed further on. Also the relative intensities of the states populated in the (p, a) reaction differ from those in the (d, r) reaction. These facts already indicate that a simple spectator model fails to explain the present data. The curves in fig. 1 have been calculated with the DWBA code DWUCK [7] with a triton cluster form factor and with the optical model parameters of refs. [8, 9]. The parameters for the triton cluster were r o = 1.25 fm and diffuseness a = 0.45 fm. Noteworthy is the small value needed for this diffuseness parameter to obtain good fits to the data. A spin-orbit interaction was only included in the proton channel. Generalising the expression of Bayman [1 ] to the case where the protons and neutrons are occupying different shells one obtains for the cross section of the (p, a) reaction
~-~)
x
= D'[~-~)DWBA" lp,l\AZ"3]
o o; *np p
Op) 0
"~--~]
" I / ' ( 2 ] p + ~ I + 1)
0
.
z
2
[ •
(1)
337
Volume 53B, number 4
PHYSICS LETTERS
23 D e c e m b e r 1974
KVI 629 10 3
--
I0 2
_
I02
102 ~ , ~
000
~
9/2*
104
129 13/2 ÷
s12-
IOI
•
i0 - ' .~ t c~ i0 I
'~ ¢•
- ' ~
0 34 I/2 -
'T~,) ,If' 1085/2+
i0~
I 45 9/2+
10¢
~
b "Io
0 60 3/2_ I0 F
I0
i0 ) _
I 14 11/2+
00
I 30
I 60
io2_
101
't ! 0
I 30
I 60
149 9/2+
_ 0
I
50
l
60
OCM Fig. 1. A n g u l a r d i s t n b u t m n s o f s t a t e s e x c a t e d in t h e l l S S n ( p , a ) l l S l n r e a c t i o n at E p = 22 MeV. T h e c u r v e s are t h e r e s u l t s o f DWBA c a l c u l a t i o n s .
Here it is assumed that the DWBA cross section does not depend on the microscopic neutron and proton configuranons; D is an overall normalisation factor which is the only free parameter. The first two terms in eq. (1) are center-of-mass corrections and the term x/(2J+ 1)/(2ip+ 1)(21+ 1) is the ratio of the three to the two partial fractional parentage coefficients. The Moshinsky bracket transforms the di-neutron with orbital angular momentum L = I and radial quantum number N and the proton to a triton with quantum numbers of c.m. motion N, L. The last bracket performs the. transformation from j/to LS .coupling. The coefficients O/L~ ~7l are the weak-coupling . . . . lp) amphtudes for coupling the proton hole lr(jp 1) to the neutron excitations of spin I to form a final state with spin J. A calculation coupling the 099/2, lpl/2, lP3/2,0t"5/2 and 0f7/2 proton holes to the zero-, one- and twophonon quadrupole and octupole vibrational states was performed to obtain the cVL~ ~71;~ . J p . is the proton • . . Jp' spectroscopic amplitude (x/~/p = ~ and the dl-neutron spectroscopic amplitude ~ is given by
:
)
× (11 ~ (il)12 } U2);lltl
12 (/)} ~ ( 0 ) ; I ) ' ( ~ 1 0 0 ;1In 1 l I n 2 12;D.
(2)
It already contains the coherence of the di-neutron configurations and can be obtained from (p, t) data through a 338
Volume 53B, number 4
PHYSICS LE'Iq'ERS
23 December 1974
KVI 575
X2
118Sn (P,Ot)il51n
13/;~ II/~ ~f/Z-
Zt/i
i/2-
9/~
50
?__. z5
0
i
-i
I,,,-
=: 25
1'4
'~ ,'2
I'o
e
~
'
b
o
EXCITATION ENERGY (llleV)
Fig. 2. Strengths of the liSSn(p, a)llSln reactmn for different signs of the relative phase of the two neutron amplitudes. The same normalisation constant was used in both eases. DWBA calculation with a cluster formfactor. For this the DX optical model parameters of ref. [3] were used. The importance of eq. (1) is that it separates proton and neutron excitations by assuming that the respective amplitudes can be independently determined. In the present case the 0 + ground state and the 2 + vibrational state dominate in the weak-coupling wave functions and the Ix/~-2÷/V~0÷I ratio was determined from a fit to the data of Fleming et al. to lie between 0.5 and 0.6. In fig. 2 the predicted (p, or) strengths (open bars) are compared with those obtained from experiment. For positive sign of the Ix/~2./x~0+l ratio (only the absolute ratio can be determined from the (p, t) experiment) there is a remarkable agreement in the relative intensities. Of special interest is the 5•2- state at 1.04 MeV which is very strongly seen in the (p, t~) reaction in agreement with theory and which in contrast is only weakly excited in the 116Sn(d ' r)115 In reaction [6]. From the calculations it follows that this state has a strong Ipi-/1 ® 2+> component. Also the ratio of the 9•2 + g.s. to the 9•2 + excited-state strength (for the 1.45 and 1.49 MeV states combined) is more than doubled compared to the (d, T) reaction due to constructive and destructive interference respectively by the Ig~/~ ® 2 +) component excited in the (p, a) reaction. Noteworthy are also the 11/2 + and 13/2 + states of the gg"f2® 2+ weak coupling quintuplet. Whereas the 13/2 + state is very strongly populated, the 11/2 + state is only weak in agreement with the theoretical predictions. The 7/2 + state has not been resolved, but the calculated number corresponds roughly to the upper limit for a possible state at 1.47 MeV in the (p, a) spectrum. To our knowledge the present analysis presents the first case in which the coherence properties of the (p, a) reaction properly have been taken into account. The striking agreement between the theoretical predictions and experiment demonstrates the usefulness of the (p, t~) reaction as a spectroscopic tool in particular for the study of weak-coupling configurations. From the cross-section ratios the relative phase of the two-neutron amplitudes can be experimentally determined. The help of Professor Arima in the derivation of the expressions for the (p, ~t) cross sections is gratefully acknowledged. We also thank Drs. W.H.A. Hesselink and S.Y. van der Werf for their assistance in the data taking. This work was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nededandse Organisatie voor Zuiver Wetenschappelijk Onderzoek" (ZWO).
339
Volume 53B, number 4
PHYSICS LETTERS
23 December 1974
References [1] B.F. Bayman, Nuclear spectroscopy with direct reactions, Vol. II, Argonne National Laboratory Report, ANL - 6878 (1964) p. 335; J.A. Nolen, Ph.D. thesis, Princeton 1965, unpublished. [2] W.R. Falk, Phys. Rev. C8 (1973) 1757, D.L. Dittmer and W.W. Daehnick, Phys. Rev. C2 (1970) 238; C. Glashausser, D L. Hendrie and E.A. McClatchie, Nucl. Phys. A222 (1974) 65; M. Vergnes, G. Rotbard, J. Kalifa and G. Berrier-Ronsin, Phys. Rev. C10 (1974) 1156. [3] D.G. Fleming, M. Blann, H.W. Fulbright and J.A. Robbins, Nucl. Phys. A151 (1970) 1. [4] P. Spmk and J.R. Erskine, Argonne National Laboratory Report ANL-PHY-1965B; J R. Comfort, Argonne Physics Division Informal Report, PHY-1970B [5] C.V. Weiffenbach and R. Tickle, Phys. Rev. C3 (1971) 1668. [6] W.H.A. Hesselink et al., Nucl. Phys. A226 (1974) 229. [7] P.D. Kunz, private commumcation. [8] C.M. Percy and F.G. Perey, Atomic Data and Nuclear Data Tables 13 (1974) 293. [91 L. McFadden and G.R. Satchler, Nucl. Phys. 84 (1966) 177.
340