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The spin isovector monopole strength and the (3He,t) reaction
Volume 219, number 2,3
PHYSICS LETTERS B
16 March 1989
THE SPIN ISOVECTOR M O N O P O L E STRENGTH AND THE ( 3 H e , t) REACTION N . AUERBACH
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel ~ and Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA F. OSTERFELD and T. UDAGAWA 2
Institute fiir Kernphysik, Kernforschunganlage Jgilieh. D-5170 Jiffich, Fed. Rep. Germany Received 4 October 1988
An analysis of the 600 MeV, 9°Zr( 3He, t )~°Nb reaction, reported earlier, is reexamined, showing that the enhanced background observed around 30 MeV excitation energy is to a large extent due to the 2he) spin-flip isovector monopole resonance. The excitation of this monopole strength is a result of the surface character of the (3He, t) reaction.
The pion charge-exchange experiments (n +, n °) were successful [ 1 ] in observing the isovector monopole resonance (IVMR). The resonances observed in this reaction are of electric type in which the spin degree of freedom is not important. The IVMR and its properties have been discussed extensively [ 2 ]. We just mention here that it is an L = 0 , T = 1 collective excitation of l p - l h nature. The l p - l h configurations correspond to 2hco excitations. The residual particle-hole (p-h) interaction is repulsive in the isovector ( T = 1 ) channel and therefore, because of the collective effect the IVMR is pushed up considerably above its unperturbed 2 h o position [ 2 ]. The transition density to the IVMR as to any monopole excitation has a characteristic shape [ 3 ]. Since the volume integral of any transition density must be zero it implies that in the case of an L = 0 transition the radial part of the transition density PM(r) has a node so that
I-4n ~ pM(r)rZdr=O.
( 1)
In fig. 1 we show the transition density for the IVMR in 9°Zr. We note that the shape ofpM is composed of a positive volume component and a negative surface
pu(r)
Fig. I. The shape of the transition density for the isovector monopole in 9°Zr.
part. A nuclear probe that is not altered by distortions of the nucleus will experience the influence of both the negative and positive parts of the transition density. The two will cancel and the cross sections for exciting a monopole state with such a kind of probe will be relatively small. In fact in the impulse approximation the excitation of a monopole state in inelastic or charge-exchange reaction would be zero in the forward direction when one neglects corrections due to the excitation energy of the monopole state. The scattering amplitude in this case is given by T= [ p M ( r ) exp(iqr) dr, d
Permanent address. On leave from the Department of Physics, University of Texas, Austin, TX 78712, USA.
184
mr
(2)
where q is the momentum transfer if one neglects the inelasticity, i.e., the excitation energy of the mon-
0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 219, number 2,3
PHYSICS LETTERS B
opole state. For q = 0, T reduces to I in eq. ( 1 ) and therefore becomes zero. In order to excite a monopole resonance one needs a strongly absorbed projectile which will not penetrate deeply into the nucleus and will not probe the volume part ofpM. The cross section will then be essentially determined only by the surface part o f this transition density, and hence may take a large value. This is precisely the reason why the (n +, n °) experiments around the (3,3) resonance energy were successful in exciting copiously the isovector monopole [ 1 ] states in various nuclei. As is well known, at these energies the pions are strongly absorbed and do not penetrate beyond the surface. Thus, they probe mostly the surface part of the transition density. When the spin degree of freedom is taken into account one may consider a J = 1 + state which involves a spin flip in addition to a monopole excitation. If we add also the isospin degree of freedom we may have a spin-isovector monopole (SIVM) state I ( L = 0 , S = 1 ), J = 1 +, r = 1 ). The aim o f the present article is to discuss possible evidences o f this mode; in particular, we shall show that the rather large background spectra observed at the forward angle ( 0 = 0 ° ) in the 9°Zr (3He, t) 9°Nb reaction at Ela b = 600 MeV are mostly due to the excitation o f this mode. The existence of such a SIVM state (or resonance) was proposed in the past [4] and its properties calculated [4,5]. The transition density for this resonance has the same characteristic radial behavior as the one shown in fig. 1. The relevant operator for the SIVM is QoJ = ~r2, air¢, ( w h e r e / z = _+ 1, 0) as compared to the electric monopole isovector operator Qo0=5~r~r~,. Therefore, as opposed to the J = 0 + electric case the
16 March 1989
SIVM has total spin J = 1 + and can in principle couple to J = 1 + states which involve L = 2 and S = 1. A realistic tensor force does actually [5] mix (to some extent) the L = 0 and L = 2 , S = 1, 2hco modes. Nuclear charge-exchange (p, n) and (n, p) reactions at intermediate energies of E = 2 0 0 - 4 0 0 MeV are very effective [ 6 - 8 ] in exciting spin degrees of freedom and were used extensively in the study of Gamow-Teller ( G T ) resonances [6]. For these energies, however, the nucleon is not a strong absorbed projectile and in view of the discussion presented above is not the most suitable probe for exciting a 2ho9 monopole transition. Nevertheless, calculations have shown [ 5 ] that the total cross section o f exciting the SIVM in Ep = 200 MeV (p, n) reactions is about 10 m b / s r for 0 = 0 ° in 9 ° Z r and about 5 m b / s r for the (n, p) reaction [9]. The cross sections for exciting the L = 1, 2 spin-flip resonances are about four times larger than for the SIVM. In 2°Spb the A T z = + 1 spin dipole component is blocked [4] and the (n, p) L = 1 transitions are very weak, one has therefore, a good chance to observe the SIVM. Indeed in a recent 2°Spb(n, p) 2°STI experiment [ 10] a peak was observed and the angular distribution, cross section and energy position when compared to
4
2
v
0
I 12
-2
S(E) (fm 4. MeV -I )
2
3
/
4
8 r(fm)
/
/
-4
-6 4
-8 -I0 0
I0
20
30
40
50
E x (MeV) Fig. 2. The distribution of the / 1 = - I spin isovector monopole
strength in 9°Zr as calculated in ref. [4 ].
Fig. 3. The transition density for the 9°Zr 2hm J= 1 + (at 29.8 MeV ) calculated in refs. [ 13,14]. 185
Volume 219, number 2,3
PHYSICS LETTERS B
theory are suggestive that it is the SIVM. Also the 9°Zr(p, n) data have been analyzed by a least-square fit multipole decomposition technique [ 11 ]. The analysis assigns 74% of the expected GT cross section up to 20 MeV excitation, an considerable J~= 1+ cross section also in the region of 20-40 MeV excitation. The deduced summed 1+ cross section up to 50 MeV is consistent with predictions for the sum GT and SIVM resonances. How can one improve the situation so as to be able to excite the ATz= - 1 component of the SIVM in reactions involving nucleon charge-exchange. One way is to increase the absorption and still utilize the strong coupling of the nucleon projectile to the spin of the target nucleon is by performing charge-exchange reactions with light ions in the energy range from 200-400 MeV per nucleon. In particular one can use the (3He, t) reaction at E3He --~600 MeV [ 12 ]. The composite 3He and t ions are strongly absorbed and the reaction takes place in the peripheral region of the target-nucleus. In fact, in a recent 9°Zr(3He, t) experiment [12] in which the Gamow-Teller (GT) resonance was studied it was observed that in the forward angle (0 = 0 ° ) the background appeared to be much larger than in the corresponding (p, n) reaction. In this paper we argue that this enhancement in the background is partly due to the excitation of the SIVM. Theoretical calculations [ 13,14] for the 9°Zr (3He, t) reaction also showed that the enhancement of the background spectra mentioned above can
16 March 1989
be interpreted very well in terms of the surface character of the (3He, t) reaction. In ref. [ 13 ] the calculations were first performed with 2he) RPA wave functions and later on in ref. [14] with 4he)-wave functions. (We found only a slight difference in the resultant final cross sections at 0=0°obtained by using either 2he) or 4he) RPA wave functions. This means that the inclusion of 4fie) states is not very important in the excitation energies considered in refs. [ 13,14 ]. ) These RPA wave functions were obtained for L = 0 , 1 and 2 spin-isospin states. The calculations produced among other states a J'~--- 1+ resonance centered around the excitation energy of Ex-~29.8 MeV. This energy is in good agreement with the energy of the SIVM predicted in an earlier calculation in ref. [4]. In the latter calculation the various spin excitations are calculated in the Hartree-Fock charge-exchange continuum RPA [4] and thus, the calculation includes all he) p-h
Radius (fm) 15
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Cut 5 fm
- -
- Cut 4 fm
\
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"2 ..a
0 0
Z
6
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I
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9
pM(r)
°,
; ~
6
9
r(fm)
20 ,)',
18
I
90
Nb MeV
- -
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Cut 3 fm
15 f
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I
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Zr(He,t) I+ E x = 298
b 25 I
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I
90
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MeV
No c u t o f f
...... '\
-~1
¢
[
I + E x = 29.8 ',
E
Rnu
i
9°Zr (p,n) 90 Nb
- - Cut 4 fm
'~
-I
-2 5 -3 0 -4
Fig. 4. The transition density for the spin isovector monopole state calculated in ref. [4] for 9°Zr.
186
I'
2
5
4-
5
Scattering Angle (deg) Fig. 5. A comparison between the (p, n) and (3He, t) differential cross sections as a function of the various higher cut-offs.
Volume 219, number 2,3
PHYSICS LETTERS B
16 March 1989
section the D W I A was employed in ref. [ 14]. The projectile-target interaction was derived from the L o v e - F r a n e y t-matrix [ 7 ]. It was found that the contribution o f the above state to the low-momentum transfer cross section was very much enhanced in the (3He, t) reaction as compared to the computed(p, n) one [14]. This is due to the fact that (3He, t) is strongly absorbed at the surface and thus, sees only the surface part of the transition density. The nucleon in (p, n) is not as strongly absorbed as 3He or t and therefore, penetrates deeper into the nucleus experiencing the two opposite sign parts of the monopole transition density. This leads to a cancellation in the (p, n) cross section by almost a factor of 10 compared to the contribution of the J = 1 + (29.8 MeV) to the (3He, t) 0 = 0 ° cross section. That this is really what is happening was checked in refs. [ 13,14 ] by varying the radial integration range in the evaluation of the cross section. In fig. 5b we present the angular distribution for the 9°Zr(3He, t)9°Nb cross section for the J = 1 + state calculated using various lower cut-off radii [ 14 ]. We see that the cross section is not changed very significantly when one introduces lower cut-offs. This really means that the 3He and triton waves do not penetrate into the nucleus
states. The coupling, however, between the various states with the same j r but different L-values (such as L - - 0 , S = 1 and L = 2 , S = 1 ) was not taken into account. The calculation produced a concentration of 2ho~ spin isovector monopole strength in all zu (12 = _+ 1, 0) channels. In fig. 2 we show the distribution of strength for the 2ho~ SIVM ( L = 0 , S = 1, J ~ = 1 + ) state in the # = - l channel. The resonance is quite wide and in this particular calculation the width is due mainly to the single-particle escape and also due to the so-called Landau spreading. The transition density of J = 1 + at 29.8 MeV as computed in ref. [ 13 ] is shown in fig. 3. It has the characteristic shape of a monopole transition density, that has a node in the surface region. As already mentioned this J = 1 + is a mixture of L = 0 ( S = 1 ) and L = 2 ( S = 1 ) excitations and not a pure L = 0 ( S = 1) SIVM as computed in ref. [4]. A comparison between the transition density in fig. 3, and the transition density for a pure L = 0, S = 1, J = 1 + obtained earlier [ 4 ] by Auerbach and Klein shown in fig. 4, indicates that the 1 + state at 29.8 MeV in ref. [13], is predominantly a monopole one. In order to calculate the contribution of the 2hm J = 1 + state to the (3He, t) as well as, the (p, n) cross
Table 1 Energy integrated cross sections (Ex ~<40 MeV) for different multipolarities j r and different scattering angles 0 (1 hco). The first row shows the 9°Zr (3He, t) and the second row the 9°Zr (p, n ) results. Also shown are the total energy integrated cross section (total) and the total energy integrated experimental cross section. GT denotes the Gamow-Teller cross section, the sum of low and high energy GT states. 0 (deg)
jr 0-
9°Zr (3He, t)
9°Zr (p, n)
0.0 0.0 2.5 7.0 4.3 12.3
9.3 1.1 9.3 3.3 5.2 0.5
0 (deg)
jr
0.0 0.0 2.5 7.0 4.3 12.8
13.7 3.1 52.9 23.8 9.6 4.0
2-
3-
16.2 6.9 74.4 28.4 26.8 10.2
1.5 0.3 9.9 2.2 14.8 6.4
0+
1+
2+
3+
9.8 5.4 0.6 0.5 0.7 0.1
314.3 110.2 44.6 17.1 15.3 6.2
37.8 4.6 45.0 10. I 14.1 10.6
45.4 5.4 65.1 12.4 36.0 15.6
Total
Experiment
444.1 138.1 338.7 99.6 167.1 61.2
487.4 163.0 335.7 131.8 205.2 89.2
GT
Total
Experiment
250.9 102.9 25.9 10.1 11.7 2.5
444.1 138.0 338.7 99.6 167.1 61.2
487.4 163.0 335.7 131.8 205.2 89.2
46.1 0.5 36.8 1.8 44.7 7.5
187
Volume 219, number 2,3
PHYSICS LETTERS B
b e y o n d the r a d i u s of 4 fm a n d therefore, are n o t affected by the change o f sign in the m o n o p o l e transition d e n s i t y . N o t so with t h e ( p , n ) cross section (see fig. 5a). The (p, n ) cross section raises sharply by factors of 3 or m o r e w h e n a lower cut-off of 4 fm is i n t r o d u c e d in the radial integration. T h i s d r a m a t i c increase is due to the fact that the cancellation that occurred w h e n there was n o cut-off, did not take place w h e n the i n n e r part o f p t r ( r ) was r e m o v e d . All these c o n s i d e r a t i o n s suggest very strongly that the excess cross section f o u n d in the b a c k g r o u n d [ 12 ] of the (3He, t) reaction a r o u n d the excitation energy of a b o u t Ex = 30 M e V is to a large extent due to spin isovector m o n o p o l e strength. We remark, h o w e v e r that there is also a n e n h a n c e m e n t of the 2hto 2 +, L = 2 a n d 3 +, L = 2 strength in the 9°Zr(3He, t) reaction over that in the 9°Zr(p, n ) reaction by a b o u t a factor o f 8. T h i s can be seen from table 1 where we show the energy integrated cross sections o f the different m u l tipoles with spin parts j r = 0 - _ j ~ = 4 - . T h e 2/~o 1 + states c o n t r i b u t e 62 m b to the (3He, t) cross section while the 2 + a n d 3 + states c o n t r i b u t e 40 m b a n d 45 (al
103~-,~i,,i,,~,,,i ,,,,,,(b) 9°Z r (~He,t)gONb
9°Zr(p,n)9°Nb
102 o
I0
I
g."
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iO °
/
J4-
.....
Io'
~ ." /4~/
". " '-...""~\~
..Q
E I0°I~,
i©"b 102
(C)
9°Zr (p, n)9°Nb
103
i i i ~ i I ~ L~ : : : :Li ; : :; :: (d)
F~
g.~
/../ ..... ....
,
100 0
6
12
9° Zr (3He,t)9°Nb
:
2 hw
I
I io°l'',--',lm,ll''l 18 O 2
,, 4
,,, 6
Scottering Angle (deg) Fig. 6. Contributions of the 1/un and 2,%~multipole strength to the 9°Zr(p,n) and 9°Zr(3He, t) energy integrated angular distributions. 188
16 March 1989
rob, respectively. The c o r r e s p o n d i n g (p, n ) cross sections are c o m p a r a t i v e l y small. T h e y are 8 mb, 4 mb, a n d 5 m b for the 2h~o 1 +, 2 +, a n d 3 + states, respectively. T h e angle d e p e n d e n c e of the energy integrated 1h~o m u l t i p o l e strength for 9°Zr (3He, t ) reactions are s h o w n in fig. 6. T h e electric isovector m o n o p o l e r e s o n a n c e was observed in a charge-exchange reaction i n v o l v i n g strongly a b s o r b e d projectiles, n a m e l y ~ 180 M e V p i o n s a n d n o w we believe that the influence o f the /~-- - 1 c o m p o n e n t o f the spin isovector m o n o p o l e r e s o n a n c e was seen in the charge-exchange reaction i n v o l v i n g the strongly a b s o r b e d 3He, t probes. O n e of us ( N . A . ) t h a n k s M. M o i n e s t e r for helpful discussions, a n d A. M e k j i a n a n d L. Z a m i c k for their hospitality at Rutgers U n i v e r s i t y where part of this work was performed.
References [ 1 ] J.D. Bowman et al., Phys. Rev. Lett. 50 (1983) 1195; A. Erell et al., Phys. Rev. C 34 (1986) 1822. [2] N. Auerbach, Nucl. Phys. A 182 (1974) 247; A.Z. Mekjian, Phys. Rev. Lett. 25 (1970) 888; A. Bohr and B.R. Mottelson, Nuclear structure, Vol. 1 (Benjamin, New York, 1979). [3] N. Auerbach, Phys. Lett. B 36 (1971) 293. [4] N. Auerbach and A. Klein, Phys. Rev. C 30 (1984) 1032. [5]A. Klein, W.G. Love and N. Auerbach, Phys. Rev. C 31 (1985) 710. [6]C.D. Goodman, Nucl. Phys. A 374 (1982) 241, and references therein. [7] W.G. Love and M.A. Franey, Phys. Rev. C 24 ( 1981 ) 1073. [8] F. Osterfeld, Phys. Rev. C 26 (1982) 762; F. Osterfeld and A. Schulte, Phys. Lett. B 138 (1984) 23; F. Osterfeld, D. Cha and J. Speth, Phys. Rev. C 31 ( 1985 ) 372. [9] A. Klein, W.G. Love, M.A. Franey and N. Auerbach, in: Proc. Intern. Conf. on Antinucleon and nucleon-nucleus interactions (Telluride, CO), eds. G.E. Walker, C.D. Goodman and C. Olmer (Plenum, New York, 1985) p. 35 I. [ 10] M.A. Moinester et al., Evidence for the spin isovector monopole resonance with 2°sPb(n, p)2°ST1 reaction. Abstract C44, XIth Intern. Conf. on Particles and nuclei (Kyoto, Japan, April 1987). [ 11 ] M.A. Moinester, Can. J. Phys. 65 (1987) 660. [ 12 ] C. Ellegaard et al., Phys. Rev. Len. 50 (1983) 1745. [ 13 ] A. Schulte, T. Udagawa, F. Osterfeld and D. Cha, Phys. Lett. B 183 (1987) 243. [ 14] T. Udagawa, A. Schulte and F. Osterfeld, Nucl. Phys. A 474 (1987) 131. [ 15 ] N. Auerbach and A. Klein, Nucl. Phys. A 395 (1983) 77.
PHYSICS LETTERS B
16 March 1989
THE SPIN ISOVECTOR M O N O P O L E STRENGTH AND THE ( 3 H e , t) REACTION N . AUERBACH
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel ~ and Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA F. OSTERFELD and T. UDAGAWA 2
Institute fiir Kernphysik, Kernforschunganlage Jgilieh. D-5170 Jiffich, Fed. Rep. Germany Received 4 October 1988
An analysis of the 600 MeV, 9°Zr( 3He, t )~°Nb reaction, reported earlier, is reexamined, showing that the enhanced background observed around 30 MeV excitation energy is to a large extent due to the 2he) spin-flip isovector monopole resonance. The excitation of this monopole strength is a result of the surface character of the (3He, t) reaction.
The pion charge-exchange experiments (n +, n °) were successful [ 1 ] in observing the isovector monopole resonance (IVMR). The resonances observed in this reaction are of electric type in which the spin degree of freedom is not important. The IVMR and its properties have been discussed extensively [ 2 ]. We just mention here that it is an L = 0 , T = 1 collective excitation of l p - l h nature. The l p - l h configurations correspond to 2hco excitations. The residual particle-hole (p-h) interaction is repulsive in the isovector ( T = 1 ) channel and therefore, because of the collective effect the IVMR is pushed up considerably above its unperturbed 2 h o position [ 2 ]. The transition density to the IVMR as to any monopole excitation has a characteristic shape [ 3 ]. Since the volume integral of any transition density must be zero it implies that in the case of an L = 0 transition the radial part of the transition density PM(r) has a node so that
I-4n ~ pM(r)rZdr=O.
( 1)
In fig. 1 we show the transition density for the IVMR in 9°Zr. We note that the shape ofpM is composed of a positive volume component and a negative surface
pu(r)
Fig. I. The shape of the transition density for the isovector monopole in 9°Zr.
part. A nuclear probe that is not altered by distortions of the nucleus will experience the influence of both the negative and positive parts of the transition density. The two will cancel and the cross sections for exciting a monopole state with such a kind of probe will be relatively small. In fact in the impulse approximation the excitation of a monopole state in inelastic or charge-exchange reaction would be zero in the forward direction when one neglects corrections due to the excitation energy of the monopole state. The scattering amplitude in this case is given by T= [ p M ( r ) exp(iqr) dr, d
Permanent address. On leave from the Department of Physics, University of Texas, Austin, TX 78712, USA.
184
mr
(2)
where q is the momentum transfer if one neglects the inelasticity, i.e., the excitation energy of the mon-
0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 219, number 2,3
PHYSICS LETTERS B
opole state. For q = 0, T reduces to I in eq. ( 1 ) and therefore becomes zero. In order to excite a monopole resonance one needs a strongly absorbed projectile which will not penetrate deeply into the nucleus and will not probe the volume part ofpM. The cross section will then be essentially determined only by the surface part o f this transition density, and hence may take a large value. This is precisely the reason why the (n +, n °) experiments around the (3,3) resonance energy were successful in exciting copiously the isovector monopole [ 1 ] states in various nuclei. As is well known, at these energies the pions are strongly absorbed and do not penetrate beyond the surface. Thus, they probe mostly the surface part of the transition density. When the spin degree of freedom is taken into account one may consider a J = 1 + state which involves a spin flip in addition to a monopole excitation. If we add also the isospin degree of freedom we may have a spin-isovector monopole (SIVM) state I ( L = 0 , S = 1 ), J = 1 +, r = 1 ). The aim o f the present article is to discuss possible evidences o f this mode; in particular, we shall show that the rather large background spectra observed at the forward angle ( 0 = 0 ° ) in the 9°Zr (3He, t) 9°Nb reaction at Ela b = 600 MeV are mostly due to the excitation o f this mode. The existence of such a SIVM state (or resonance) was proposed in the past [4] and its properties calculated [4,5]. The transition density for this resonance has the same characteristic radial behavior as the one shown in fig. 1. The relevant operator for the SIVM is QoJ = ~r2, air¢, ( w h e r e / z = _+ 1, 0) as compared to the electric monopole isovector operator Qo0=5~r~r~,. Therefore, as opposed to the J = 0 + electric case the
16 March 1989
SIVM has total spin J = 1 + and can in principle couple to J = 1 + states which involve L = 2 and S = 1. A realistic tensor force does actually [5] mix (to some extent) the L = 0 and L = 2 , S = 1, 2hco modes. Nuclear charge-exchange (p, n) and (n, p) reactions at intermediate energies of E = 2 0 0 - 4 0 0 MeV are very effective [ 6 - 8 ] in exciting spin degrees of freedom and were used extensively in the study of Gamow-Teller ( G T ) resonances [6]. For these energies, however, the nucleon is not a strong absorbed projectile and in view of the discussion presented above is not the most suitable probe for exciting a 2ho9 monopole transition. Nevertheless, calculations have shown [ 5 ] that the total cross section o f exciting the SIVM in Ep = 200 MeV (p, n) reactions is about 10 m b / s r for 0 = 0 ° in 9 ° Z r and about 5 m b / s r for the (n, p) reaction [9]. The cross sections for exciting the L = 1, 2 spin-flip resonances are about four times larger than for the SIVM. In 2°Spb the A T z = + 1 spin dipole component is blocked [4] and the (n, p) L = 1 transitions are very weak, one has therefore, a good chance to observe the SIVM. Indeed in a recent 2°Spb(n, p) 2°STI experiment [ 10] a peak was observed and the angular distribution, cross section and energy position when compared to
4
2
v
0
I 12
-2
S(E) (fm 4. MeV -I )
2
3
/
4
8 r(fm)
/
/
-4
-6 4
-8 -I0 0
I0
20
30
40
50
E x (MeV) Fig. 2. The distribution of the / 1 = - I spin isovector monopole
strength in 9°Zr as calculated in ref. [4 ].
Fig. 3. The transition density for the 9°Zr 2hm J= 1 + (at 29.8 MeV ) calculated in refs. [ 13,14]. 185
Volume 219, number 2,3
PHYSICS LETTERS B
theory are suggestive that it is the SIVM. Also the 9°Zr(p, n) data have been analyzed by a least-square fit multipole decomposition technique [ 11 ]. The analysis assigns 74% of the expected GT cross section up to 20 MeV excitation, an considerable J~= 1+ cross section also in the region of 20-40 MeV excitation. The deduced summed 1+ cross section up to 50 MeV is consistent with predictions for the sum GT and SIVM resonances. How can one improve the situation so as to be able to excite the ATz= - 1 component of the SIVM in reactions involving nucleon charge-exchange. One way is to increase the absorption and still utilize the strong coupling of the nucleon projectile to the spin of the target nucleon is by performing charge-exchange reactions with light ions in the energy range from 200-400 MeV per nucleon. In particular one can use the (3He, t) reaction at E3He --~600 MeV [ 12 ]. The composite 3He and t ions are strongly absorbed and the reaction takes place in the peripheral region of the target-nucleus. In fact, in a recent 9°Zr(3He, t) experiment [12] in which the Gamow-Teller (GT) resonance was studied it was observed that in the forward angle (0 = 0 ° ) the background appeared to be much larger than in the corresponding (p, n) reaction. In this paper we argue that this enhancement in the background is partly due to the excitation of the SIVM. Theoretical calculations [ 13,14] for the 9°Zr (3He, t) reaction also showed that the enhancement of the background spectra mentioned above can
16 March 1989
be interpreted very well in terms of the surface character of the (3He, t) reaction. In ref. [ 13 ] the calculations were first performed with 2he) RPA wave functions and later on in ref. [14] with 4he)-wave functions. (We found only a slight difference in the resultant final cross sections at 0=0°obtained by using either 2he) or 4he) RPA wave functions. This means that the inclusion of 4fie) states is not very important in the excitation energies considered in refs. [ 13,14 ]. ) These RPA wave functions were obtained for L = 0 , 1 and 2 spin-isospin states. The calculations produced among other states a J'~--- 1+ resonance centered around the excitation energy of Ex-~29.8 MeV. This energy is in good agreement with the energy of the SIVM predicted in an earlier calculation in ref. [4]. In the latter calculation the various spin excitations are calculated in the Hartree-Fock charge-exchange continuum RPA [4] and thus, the calculation includes all he) p-h
Radius (fm) 15
I
I
I0
- "
Cut 5 fm
- -
- Cut 4 fm
\
5
"2 ..a
0 0
Z
6
!
I
30
9
pM(r)
°,
; ~
6
9
r(fm)
20 ,)',
18
I
90
Nb MeV
- -
No c u t o f f
......
Cut 3 fm
15 f
15
I
3
Zr(He,t) I+ E x = 298
b 25 I
12
I
90
o
MeV
No c u t o f f
...... '\
-~1
¢
[
I + E x = 29.8 ',
E
Rnu
i
9°Zr (p,n) 90 Nb
- - Cut 4 fm
'~
-I
-2 5 -3 0 -4
Fig. 4. The transition density for the spin isovector monopole state calculated in ref. [4] for 9°Zr.
186
I'
2
5
4-
5
Scattering Angle (deg) Fig. 5. A comparison between the (p, n) and (3He, t) differential cross sections as a function of the various higher cut-offs.
Volume 219, number 2,3
PHYSICS LETTERS B
16 March 1989
section the D W I A was employed in ref. [ 14]. The projectile-target interaction was derived from the L o v e - F r a n e y t-matrix [ 7 ]. It was found that the contribution o f the above state to the low-momentum transfer cross section was very much enhanced in the (3He, t) reaction as compared to the computed(p, n) one [14]. This is due to the fact that (3He, t) is strongly absorbed at the surface and thus, sees only the surface part of the transition density. The nucleon in (p, n) is not as strongly absorbed as 3He or t and therefore, penetrates deeper into the nucleus experiencing the two opposite sign parts of the monopole transition density. This leads to a cancellation in the (p, n) cross section by almost a factor of 10 compared to the contribution of the J = 1 + (29.8 MeV) to the (3He, t) 0 = 0 ° cross section. That this is really what is happening was checked in refs. [ 13,14 ] by varying the radial integration range in the evaluation of the cross section. In fig. 5b we present the angular distribution for the 9°Zr(3He, t)9°Nb cross section for the J = 1 + state calculated using various lower cut-off radii [ 14 ]. We see that the cross section is not changed very significantly when one introduces lower cut-offs. This really means that the 3He and triton waves do not penetrate into the nucleus
states. The coupling, however, between the various states with the same j r but different L-values (such as L - - 0 , S = 1 and L = 2 , S = 1 ) was not taken into account. The calculation produced a concentration of 2ho~ spin isovector monopole strength in all zu (12 = _+ 1, 0) channels. In fig. 2 we show the distribution of strength for the 2ho~ SIVM ( L = 0 , S = 1, J ~ = 1 + ) state in the # = - l channel. The resonance is quite wide and in this particular calculation the width is due mainly to the single-particle escape and also due to the so-called Landau spreading. The transition density of J = 1 + at 29.8 MeV as computed in ref. [ 13 ] is shown in fig. 3. It has the characteristic shape of a monopole transition density, that has a node in the surface region. As already mentioned this J = 1 + is a mixture of L = 0 ( S = 1 ) and L = 2 ( S = 1 ) excitations and not a pure L = 0 ( S = 1) SIVM as computed in ref. [4]. A comparison between the transition density in fig. 3, and the transition density for a pure L = 0, S = 1, J = 1 + obtained earlier [ 4 ] by Auerbach and Klein shown in fig. 4, indicates that the 1 + state at 29.8 MeV in ref. [13], is predominantly a monopole one. In order to calculate the contribution of the 2hm J = 1 + state to the (3He, t) as well as, the (p, n) cross
Table 1 Energy integrated cross sections (Ex ~<40 MeV) for different multipolarities j r and different scattering angles 0 (1 hco). The first row shows the 9°Zr (3He, t) and the second row the 9°Zr (p, n ) results. Also shown are the total energy integrated cross section (total) and the total energy integrated experimental cross section. GT denotes the Gamow-Teller cross section, the sum of low and high energy GT states. 0 (deg)
jr 0-
9°Zr (3He, t)
9°Zr (p, n)
0.0 0.0 2.5 7.0 4.3 12.3
9.3 1.1 9.3 3.3 5.2 0.5
0 (deg)
jr
0.0 0.0 2.5 7.0 4.3 12.8
13.7 3.1 52.9 23.8 9.6 4.0
2-
3-
16.2 6.9 74.4 28.4 26.8 10.2
1.5 0.3 9.9 2.2 14.8 6.4
0+
1+
2+
3+
9.8 5.4 0.6 0.5 0.7 0.1
314.3 110.2 44.6 17.1 15.3 6.2
37.8 4.6 45.0 10. I 14.1 10.6
45.4 5.4 65.1 12.4 36.0 15.6
Total
Experiment
444.1 138.1 338.7 99.6 167.1 61.2
487.4 163.0 335.7 131.8 205.2 89.2
GT
Total
Experiment
250.9 102.9 25.9 10.1 11.7 2.5
444.1 138.0 338.7 99.6 167.1 61.2
487.4 163.0 335.7 131.8 205.2 89.2
46.1 0.5 36.8 1.8 44.7 7.5
187
Volume 219, number 2,3
PHYSICS LETTERS B
b e y o n d the r a d i u s of 4 fm a n d therefore, are n o t affected by the change o f sign in the m o n o p o l e transition d e n s i t y . N o t so with t h e ( p , n ) cross section (see fig. 5a). The (p, n ) cross section raises sharply by factors of 3 or m o r e w h e n a lower cut-off of 4 fm is i n t r o d u c e d in the radial integration. T h i s d r a m a t i c increase is due to the fact that the cancellation that occurred w h e n there was n o cut-off, did not take place w h e n the i n n e r part o f p t r ( r ) was r e m o v e d . All these c o n s i d e r a t i o n s suggest very strongly that the excess cross section f o u n d in the b a c k g r o u n d [ 12 ] of the (3He, t) reaction a r o u n d the excitation energy of a b o u t Ex = 30 M e V is to a large extent due to spin isovector m o n o p o l e strength. We remark, h o w e v e r that there is also a n e n h a n c e m e n t of the 2hto 2 +, L = 2 a n d 3 +, L = 2 strength in the 9°Zr(3He, t) reaction over that in the 9°Zr(p, n ) reaction by a b o u t a factor o f 8. T h i s can be seen from table 1 where we show the energy integrated cross sections o f the different m u l tipoles with spin parts j r = 0 - _ j ~ = 4 - . T h e 2/~o 1 + states c o n t r i b u t e 62 m b to the (3He, t) cross section while the 2 + a n d 3 + states c o n t r i b u t e 40 m b a n d 45 (al
103~-,~i,,i,,~,,,i ,,,,,,(b) 9°Z r (~He,t)gONb
9°Zr(p,n)9°Nb
102 o
I0
I
g."
/ /
iO °
/
J4-
.....
Io'
~ ." /4~/
". " '-...""~\~
..Q
E I0°I~,
i©"b 102
(C)
9°Zr (p, n)9°Nb
103
i i i ~ i I ~ L~ : : : :Li ; : :; :: (d)
F~
g.~
/../ ..... ....
,
100 0
6
12
9° Zr (3He,t)9°Nb
:
2 hw
I
I io°l'',--',lm,ll''l 18 O 2
,, 4
,,, 6
Scottering Angle (deg) Fig. 6. Contributions of the 1/un and 2,%~multipole strength to the 9°Zr(p,n) and 9°Zr(3He, t) energy integrated angular distributions. 188
16 March 1989
rob, respectively. The c o r r e s p o n d i n g (p, n ) cross sections are c o m p a r a t i v e l y small. T h e y are 8 mb, 4 mb, a n d 5 m b for the 2h~o 1 +, 2 +, a n d 3 + states, respectively. T h e angle d e p e n d e n c e of the energy integrated 1h~o m u l t i p o l e strength for 9°Zr (3He, t ) reactions are s h o w n in fig. 6. T h e electric isovector m o n o p o l e r e s o n a n c e was observed in a charge-exchange reaction i n v o l v i n g strongly a b s o r b e d projectiles, n a m e l y ~ 180 M e V p i o n s a n d n o w we believe that the influence o f the /~-- - 1 c o m p o n e n t o f the spin isovector m o n o p o l e r e s o n a n c e was seen in the charge-exchange reaction i n v o l v i n g the strongly a b s o r b e d 3He, t probes. O n e of us ( N . A . ) t h a n k s M. M o i n e s t e r for helpful discussions, a n d A. M e k j i a n a n d L. Z a m i c k for their hospitality at Rutgers U n i v e r s i t y where part of this work was performed.
References [ 1 ] J.D. Bowman et al., Phys. Rev. Lett. 50 (1983) 1195; A. Erell et al., Phys. Rev. C 34 (1986) 1822. [2] N. Auerbach, Nucl. Phys. A 182 (1974) 247; A.Z. Mekjian, Phys. Rev. Lett. 25 (1970) 888; A. Bohr and B.R. Mottelson, Nuclear structure, Vol. 1 (Benjamin, New York, 1979). [3] N. Auerbach, Phys. Lett. B 36 (1971) 293. [4] N. Auerbach and A. Klein, Phys. Rev. C 30 (1984) 1032. [5]A. Klein, W.G. Love and N. Auerbach, Phys. Rev. C 31 (1985) 710. [6]C.D. Goodman, Nucl. Phys. A 374 (1982) 241, and references therein. [7] W.G. Love and M.A. Franey, Phys. Rev. C 24 ( 1981 ) 1073. [8] F. Osterfeld, Phys. Rev. C 26 (1982) 762; F. Osterfeld and A. Schulte, Phys. Lett. B 138 (1984) 23; F. Osterfeld, D. Cha and J. Speth, Phys. Rev. C 31 ( 1985 ) 372. [9] A. Klein, W.G. Love, M.A. Franey and N. Auerbach, in: Proc. Intern. Conf. on Antinucleon and nucleon-nucleus interactions (Telluride, CO), eds. G.E. Walker, C.D. Goodman and C. Olmer (Plenum, New York, 1985) p. 35 I. [ 10] M.A. Moinester et al., Evidence for the spin isovector monopole resonance with 2°sPb(n, p)2°ST1 reaction. Abstract C44, XIth Intern. Conf. on Particles and nuclei (Kyoto, Japan, April 1987). [ 11 ] M.A. Moinester, Can. J. Phys. 65 (1987) 660. [ 12 ] C. Ellegaard et al., Phys. Rev. Len. 50 (1983) 1745. [ 13 ] A. Schulte, T. Udagawa, F. Osterfeld and D. Cha, Phys. Lett. B 183 (1987) 243. [ 14] T. Udagawa, A. Schulte and F. Osterfeld, Nucl. Phys. A 474 (1987) 131. [ 15 ] N. Auerbach and A. Klein, Nucl. Phys. A 395 (1983) 77.