- Email: [email protected]
Excitation of isovector modes in heavy ion induced charge exchange reactions
Nuclear PhysicsA482(1988) 357c-372c North-Holland,Amsterdam
357c
EXCITATION OF ISOVECTOR MODES IN HEAVY ION INDUCED CHARGE EXCHANGE REACTIONS*
W. von Oertzen Hahn-Meitner-lnstitut Berlin GmbH, 1000 Berlin 39, Germany and Fachbereich Physik, Freie Universit~t Berlin
Charge exchange reactions induced by 12C and 13C in the "(p,n)" and "(n,p)" direction have been studied in the energy range of 20 MeV/u to 70 MeV/u. The (12C, 12N) is particularly selective, it populates only (as = 1) spinflip states. The (13C, 13N) populates non spin-flip modes. Due to momentum transfers determined by Qvalues, the (12C, 12N) populates strongly Dipole transitions. Spin-flip Giant Resonances in 12C, 160, 40Ca, 44Ca and 58Ni are observed.
1. INTRODUCTION
Heavy ions offer a great variety of choices to induce charge exchange reactions which can be used to study isovector resonances in nuclei, Of particular importance are possibilities for the "(n,p)" transitions and double charge exchange which have so far been studied only in situations with rather strong experimental limitations namely induced by pions (1,2) and secondary neutron beams (3,4). We will focuss our attention to the light heavy ions, because they offer the best conditions with respect to experimental properties. We report here results of studies done with 12C and 13C projectiles at energies of 20 MeV/u up to 70 MeV/u. These results were obtained using magnetic spectrometers at the accelerator VlCKSI (HMI, Berlin), SARA (Grenoble) and GANIL (Caen).
Several questions can be addressed with these reactions: i) Evolution of the reaction mechanism as function of incident energy from two-step nucleon transfer to meson exchange. ii) Quantitative description of the cross-section in its dependence on momentum transfer.
Collaboration supported by PROCOPE:HMI/FU: H.G.Bohlen, E. Stiliaris,W. von Oertzen, S. Kubono; ISN, Grenoble: C. Berat, M. Buenerd, J.Y. Hostachy, Ph. Martin; CEN,Saclay:A. Miczaika (sup. by DFG),B. Fernandez,J. Barrette,B. Berthier;GANIL:W. Mittig 0375-9474/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
358c
HI. yon Oertzen / Excitation o f isovector modes
iii)
Selectivity for spinflip and non-spinflip transitions in relation to the GamovTeller and Fermi-transitions in nuclear p-decay.
iv)
Localisation and study of the properties of isovector "Giant" resonances with and without spinflip. We are only at the beginning of this venture and work from other laboratories is progressing along the same lines (5). Among the variety of choices of projectiles we will focus on the 12C and 13C nuclei. The most important property of the charge exchange reactions independent of the mechanism is the momentum transfer q due to the incoming and outgoing momenta ki and kf
-~ =-~-'~f.
(1)
We neglect the distortions due to the Coulomb and nuclear potentials and use the asymptotic values of the momenta in the initial (ki) and final (kf) channels. With this momentum transferred to the whole nucleus at the interaction radius Rint we obtain the preferential excitation of the multipole resonances with a multipolarity L, given by L= q
• Rint.
(2)
We have listed in table 1 the momentum transfer for different reactions and Qvalues at 70 MeV/u. The momentum transfer at 0° (it is minimum here) is given mainly by the Q-value, because there is no mass transfer in a direct charge exchange reaction: q = 0.11Q/x/-~-~
(3)
Here the incident energy per nucleon E/A and the Q-value are both in MeV and q is obtained in units of fm-1 In order to excite the modes with the lowest multipolarity we need the smallest Qvalues, or for given Q-values the highest possible incident velocity (in v'MeV/u). The variation of q with angle is of course very strong, if ki is large; typical variations of q with angle are given in table 1. The property described by equation 3, is common to all "inelastic" processes where no mass is transferred (6). A further important property which determines the reaction mechanism, is the momentum transfer in the quasi free reactions on a nucleon in the target which is given e.g. by the qvalues for p (12C, 12N)n as shown in table 1.
W. von Oer tzen / Excitation o f isovector modes
T a b l e 1.
The momentum transfers q using the assymptotic values of the m o m e n t a ki a n d k f a r e g i v e n f o r d i f f e r e n t reactions, reaction angles and Q-values.
~°Ca(12Cr 12NTI2B)
and 40Ca (13C~
a t EL:7OMeV/u Reaction Qo-values
q in [fm -l] 130 MeV/u
12 C
~Oca
~8Ca
90Z£
Qo[MeV]
-18,1
-30.7
-18.6
-29.3
-19.6
GO
0.25
0.41 0.45
0.24 0.38
0.39 0.49
0.26 0.42 O. 72
1°
Ex=10 HeY Go 1° 2o 5o
Qo[MeV] 0o
i° 2° 5o
Ex=lO MeV
~-
Go
v
1°
So Qo[Mev] GO lO° Ex=lO MeV •
13N) c e a c t i o n s
Target P
•
359c
0o 10°
O. 55
0.63
O. 72
0.29
1.02
1.48
1.56
1.70
-28,1
-40.7
-28.6
-39.3
-29.6
0.42
0.54 0.57 O. 66 1.08
0.38 0.48 0.70 1.50
0.52 0.60 O. 80 1.60
0.39 0.51 O. 77 1.72
0.44 -0.3
-15.6
-).5
-14.2
-4.5
O. 04 0.05 0.07 0.15
0.21 0.28 0.44 1.01
0.05 0.31 0.62 1.56
0.19 0.37 0.67 1.63
0.06 0.37 0.73 1.81
9Oz£
0.40 0.45 O. 59 1.16
0.61 0,64 O. 74 1.24
0.09 0.25 0.48 1.19
-13.0
-25.6
-13.5
-24.2
-14.5
0.18 0.18 0.19 0.22
0.34 O. 39
0.18 O. ]6
0.32 O. 45
0,19 O. 41
0.29 O. 37
0.52
0.65
0.72
0.73
0.55
1.04
1.56
1.65
1,81
1.21
_
0.0
-12.5
-0.53
-11.2
-1.50
0.00 0.08 0.16
0.17 0.22 0.33
0,01 0.15 0,31
0.15 0.21 0.33
0,02 0,16 0,31
-22.5
-10,5
-21.2
-11.5
0.33 0.35 0.42
0,14 0,20 0.33
0.30 0.34 0.41
0.16 0.22 0.34
The same kinematics holds for "(p, n ~" reaction given the same Q-values
0.03 0.11 0.21
0.26 0.27 0.32
360c
IV. yon Oertzen / Excitation o f &ovector modes
It is obvious from table 1 that for low multipolarities (L = 0, isovector monopol, and Gamov-Teller resonances), reactions like (p,n) or in,p) and also (t, 3He) as well as (13C, 13N) are well suited. We also find, that at the energies discussed here (20 MeV/u to 70 MeV/u) in the reactions involving 12C the L=0 resonances will be suppressed, because of the large momentum transfer q due to the Q-values incountered in the transitions. In addition to the considerations of the favoured multipolarity L, given by q • R, we have to consider the form factors in momentum space. Collectivity in nuclear states can be observed at low momentum transfer for 1" states due to the repulsive properties of the nucleon-nucleon interaction at small q. Collectivity can also be attained for states of low spin and unnatural parity (e.g. 2-) at high momentum transfer at typically twice the pion mass of ~ 2.3 fro-l, because of the attractive "properties of nucleon-nucleon interaction at large q (ref. 7,8). Form factors for 2" states (L= 1) may have large momentum components beyond the simple value of q given by q = L/R which for 40Ca is 0.2 fm-1 (R = 5 fm). For the collectivity at large momentum transfer of q ~ 2.3 fro-l, we have to face the problem of strong reduction of the cross section because of the scattering of the projectiles in the mean field of the target nucleus which decays fast with scattering angle (momentum transfer). In many experiments (VICKSI and GANIL) it was possible to make measurements around eL = 0 ° with the full solid angle of the magnetic spectrometer, the primary beam being stopped behind the first dipole at VlCKSl and GANIL The angular information was than obtained by the time of flight (VICKSI) or by ray tracing techniques (GANtL). Measurements around 0° turned out to be very important, not only in order to minimize the momentum transfer q, but also because the angular distributions show only in close vicinity to 0° characteristic differences for different multipolarities L.
II. PROPERTIES OF THE 12C A N D 13C INDUCED REACTIONS
a) Selectivity, reactions on 12Cand 160 A study of the (12C, 12N) and (13C, 13N) reactions at 30 MeV/u on the 12C and 160 targets showed an extreme difference in selectivity of final states (9). Fig. 1 shows two spectra of the two reactions on 12C at 30 MeV/u. We note the extreme difference in the population of final states. Fig. 2 shows a series of spectra of the (12C, 12N) reaction at 70 MeV/u. The two prominent peaks correspond to well
W. von Oertzen / Excitation o f isovector modes
361c
known states in 12B, the 1 + (ground state), and to the 2, 4°states at 4.37 MeV and 4.52 MeV (they are above the particle emission threshold). The structure observed at 7.8 MeV we attribute to the 1°state of the spin-dipole resonance which is mainly manifest in the 2- state at 4.4 MeV and possibly further strength (0- 1") at 10.3 MeV. The 1- state is quite narrow, its width of ~ 10 MeV is about 4 times the experimental resolution and is different from the 1- GDR observed in the case of (13C, 13N).
250
c3
~O C~
12C(12C,12N)12B
20C
Eiob = 358.4 MeV
15C
E)I:b = 3.4 o A® : 0 . 6 °
t C~ t
>
i Q_ i
10C 5C C 60C 50C
[=*b = 379.1 MeV ®~°== o , 0 o
~ _
~ ~'
I1 ~J
~-
40C 50C 200 100 0
16
12
8 E, [MeV]
4
0
Fi.q. 1 :Spectra of (12C, 12N) and (13C, 13N) reactions on 12C at 30 MeV/u. The systematic feature (in fig. 2) of the three states with decreasing cross section (4.37 MeV (2"), 7.8 MeV (1") and ca. 10 MeV (0")) suggests that the 2, 1, 0"members of the spinflip dipole are all observed; they have decreasing collectivity because of the possibilities to mix configurations, the absence of the broad structure due to the GDR which is observed in the (13C, 13N) case is rather remarkable. It shows that the GDR is not excited by a spinflip interaction. The dominance of the unnatural parity states in the case of (12C, 12N) is very large and we will assume that this conclusion is valid also for heavier targets (sect. III and IV).
W. yon Oertzen / Excitation of isovector modes
362c
t l
12C(12C,12N)12B EL=70HeV/u
0
10
20
30
40 -10 E,[MeV]
0
10
!
20
30
40
Fiq. 2: Spectra of (12C, 12N) reactions on 12C at 70 MeV/u.
2000 ~- I |
12C(12C12B)12N ELab=840MeV Qo=-30.70MeV
,
~ ~ ,
'~Lab=0.95°±0-16 °
300012C(I~J2N)128
lo
ELa~ 840,M~'V
20001
Qo40.70~V
.
"'~Lab=0.95%0-16°
L 0
5
10 15 20 Ex (MeV)
25
30
35
Fiq. 3: Comparison of (12C, 12N) and (12C, 12B) reactions on 12C at 70 MeV/u.
14I. yon Oertzen / Excitation o f isovector modes
363c
Comparing the (12C, 12N) and (12C, 12B) reactions in fig. 3 we find some differences, which we must attribute to the additional population of bound states in the case of the ejectile 12B. The two reactions populating the ground states of 12N and 12B are mirror reactions which must have the same cross sections. The additional structure observed at ca. 2.1 MeV excitation in the 12B spectrum indicates that the 2 ÷ states in both nuclei are excited ("mutual excitation"). This is suggested by the strong population of the 2 + state in the non spinflip reaction (13C, 13N) shown in fig. 1. The strong restrictive selectivity is lost in the (12C, 12B2+) branch and a larger class of states (as = 0 and as = 1) in the residual nucleus can be excited with considerable cross section, although this branch is smaller than the (12C, 12B1 + ) transition. This gives us some indication also to differences observed in the (12C, 12N) and (12C, 12B) spectra, in particular the continuum at higher excitation energies is more than a factor 2 higher in the case of 12B ejectiles (sect. IV).
105
_10 ~
i
102
101
10 0
-I0°
O'
0m
IO°-I0°
O°
0
10°
Fiq. 4: Angular distributions of transitions 12C(13C, 13N)12B at 30 MeV/u, the curves are one-step and two-step DWBA-calculations. The angular distribution for the most prominent transitions on the 12C-target are shown in figs. 4 and 5. In fig. 4 the left side shows calculations (ref. 9) at 30 MeV/u using the coupled reaction channel approach and two-step proton-neutron transfer. A very large space of configurations up to 2 he0 excitations had to be
364c
14/. yon Oertzen / Excitation o f isovector modes
included in order to obtain agreement with the data. The overall normalisation is given by the factor N2 and is in the range 4 to 10. The right hand side shows calculations with o~- direct charge exchange interaction without tensor interaction. There is a distinct difference in shape, which favours the assumption that at this energy the two-step transfer is strong and dominating for certain transitions at this energy. We notice that there is little oscillatory structure in the data at 70 MeV/u as opposed to the prediction of most simple one-step calculations. The unnatural parity states (spinflip states) are dominantly populated by the tensor interaction (10,11), and this may be the reason for the absence of diffraction structures. A characteristic feature, which shows dependence on the multipolarity, appears to be the position of the first maximum around 0° and thus the width of the angular peak around 0°
!
I
I
I
I
I
I
I
1000
1000
/ ~
[0.667÷0.77] *~
100
1=*,3+
L
~ 1000
+**
+,
÷
**
**
4'
"~100
[~.251 2, o
+ + '
$
+* * +
%0.
[1"7]'2+
lOO
$
10C
+
÷÷
[781
100(
++Ca112C,12BlU.Sc
+
Et:7OMeVlu 10(
\t
$
+
'i'
12C 1 (2C 12 'Z B lN l ~ EL=7OMeV uI i
' _; ° " o
°
. . 2. .0 . eCM
4o
+."
I
-2°-10
I
I
I
l
I
o°
1°
2°
3°
+0
eCM
Fig. 5: Same as Fig. 4 for 70 MeV/u for 12C and 44Ca targets. The curves are drawn to uide the eye. Note the similarity of the L=0 distributions for the t w o ifferent targets. Concerning the reaction mechanism the absolute prediction of cross sections needs further detailed work. Because of the internal momentum mismatch in transfer reactions for higher energies (6), we can expect that at energies of 50 to 70 MeV/u
IV. yon Oertzen / Excitation o f isovector modes
365c
the one-step charge exchange (meson exchange) dominates over the two-step transfer. III. (13C, 13N) AND (13C, 13B) REACTIONS AT 30 MEV/u The (13C, 13N) reaction should preferentially excite the non spinflip isovector modes. The most prominent one is the T> Giant Tipole Resonance (GDR) (L= 1), which is well observed at small angles (fig. 6). As already discussed with the results at 30 MeV/u (ref. 12) the (13C, 13B) reaction populates both spinflip (As = 1) and non spinflip (As = 0) transitions, however, the As = 1 transitions dominate. In both spectra shown in fig. 6 we see yield on top of a background beyond the GDR, which we interprete as the isovector quadrupol resonance.
p(13C,13N)n lZC(13C13N)lZB 2+{0.95MeV}
12C(13Co13B]lZN I EL=30MeVlUeL=IJ[8' *
60.0
I
300 -
I
1
2-,SFGDR{/,.2 HeY)
2
1*
.
200
300
/,00
pl
.
t, 100 CHANNELS
.
200
.
.
300
/,00
Fig. 6: (13C, 13N) and (13C, 13B) spectra on 12C target at 30 MeV/u. In fig. 7 we show spectra of the (13C, 13B) and (13C, 13N) reactions on 90Zr at 30 MeV/u. For the case of the "(p,n)" reaction we have used the results of previous work (13) and of calculations of Osterfeld (14) for the position of the resonances with multipotarity L=0, L= 1 and L= 2. With these assumptions we are able to describe the main intensity of the observed "bump" in the (13C, 13B) spectrum, with a remaining background, which we attribute to three body reactions. A similar attempt to fit was done for the (13C, 13N)) spectrum (fig. 7b). Fig. 7 also shows the differences between normalised spectra for both cases in order to emphasize the differences between spectra at small and at larger angles. We
366c
W. yon Oertzen / Excitation o f isovector modes
believe t h a t w i t h these differences the L = 1 and L = 2 strength is most likely singled out. The contributions from L = 0 are rather strongly suppressed as compared to (p,n) reactions due to the large m o m e n t u m transfers q as can easily be deduced f r o m table 1.
200
E~tM,vl .
90Nb
~ ~
+o '
9OZr(13 C 13B)9ONb 30MeV/u
eL:I.8°
Ioo
~
0
100
0m
,I ,4
PiI3C,I~N}~N~n r{
200 ~ ~
+
.
, ~ n
I00
~,,~" r'fl ll~jI
=. o
"~~00 g
.,.
100
~OZr(13C 13N)9O Y 30MeVlu
300
87
30 1~?~3,.+,s+~,o_
j
lO0~ 0 --
100
Fiq. 7aab:
'
+ 200 300 chcznnets
400
200
300 400 channels
(13C, 13B) and (13C, 13N) spectra on 90Zr at 30 MeV/u.
Vl. R E S U L T S F O R (12C, 12N) A N D (12C, 128) R E A C T I O N a t 7 0 M E V / u
In this chapter we show preliminary results of a study of "(n, p)" and "(p, n)" transitions studied at 70 MeV/u. The results on the targets 12C and 160 have shown t h a t the (12C, 12N) reaction produces d o m i n a n t l y final states w i t h As = 1 - t h a t is states w i t h unnatural parity n = (-)J ÷ 1 This feature enables us to discuss the results of reactions also for cases where the final states are not completely resolved.
a) 40Ca (12C, 12N or 12B) at 70 MeV/u These spectra were taken w i t h the spectrometer SPEG at GANIL w i t h an overall resolution of ~300 keV. A study of the 40Ca (p,n)40Sc (ref. 15) reaction at E = 134
367c
W. yon Oertzen/ Excitation of isovector modes
MeV allows us to identify the main low lying groups in the 40Ca (12C, 12B) reaction (fig. 8). The rather weak ground state group consists of a 3- and 4- state at 0.0 and 0.03 MeV; in our case we can identify this peak w i t h a L=3, As = 1 (J,, = 4 °) transition (d3/2 -~ f7/2). The d o m i n a n t peak in the spectrum consists of a 2- and 5state. We can assume t h a t it is characterised by L= 1, As = 1 (J,, = 2") transitions (d3/2 -. p3/2). The a n g u l a r d i s t r i b u t i o n s of these t w o groups clearly s h o w a difference which can be directly related to the momentum transfer (see table 1).
200 ,oo~ i
~
316°*-°160 =
I 2oo,I-
l
= 2oo~-
~
~°Cn(12C12B)~°Sc i EL:70~leV/u I e'--°32°-*°16° I
~
200
'~
200
20( )
;
0.63 °
'=
0.96°
I0C
o
6
. . . . . . . . . . . . . .
o
'. "~' ;; ' i'~ '
~
' ~
' *
' ~
' ~
'
~,
~ooto
I_
I
'
26°
1
6-
"
100
.......................................
~oo,L ' ;~::~.°
" ° " " ;.;/°"
E K [ MeV ]
Fiq. 8: Spectra of the (12C, 12N) and ,oo~- z ~ ~ _ . (12C, 12B) reactions on 40Ca . . . . . . . . . . . . . . . . .
"~--~
£,[MeVl
In fig. 9 w e show in addition the angular d i s t r i b u t i o n s of the c o r r e s p o n d i n g transitions in the (12C, 12N) reaction. For the case of an N = Z t a r g e t the t w o reactions should give identical results - because of charge symmetry. There is however, a difference in momentum transfer. The m o m e n t u m transfer of ca. 0.25 0.35 fm-1 at zero degrees suggests that the L = 1 angular distributions should give a maximum at 0 °. We actually observe a peak at almot 0 ° for the 2-transition,
368c
W. yon Oertzen / Excitation of isovector modes
w h e r e a s t h e group which we attribute to the 4-state shows a maximum at 1.0 °. At this angle the m o m e n t u m transfer is already 0.5 - 0.6 fm-1 ; w i t h a nuclear radius of ca. R = 5 fm we clearly obtain o p t i m u m conditions from q • R for L = 3. We notice a difference in the shape of the group at 0.9 MeV excitation, which in the case of (12C, 12N) is a pure 2"state, and in the case of (12C, 12B) contains the 12B2+ transition w i t h an angular m o m e n t u m transfer of L = 3. I
I
I
I
I
I
I
[GS.0.03]
~-,3100 <'÷
' Ii'
t
,~,÷ +
O
**
I
,
[0.7/,.0.891 =2-,5-
O
[0.7/*,0.891
2__-,5-
100
O
i
_i °
i
J
0o
i°
ecM
i
2°
i
3°
~OCo(lZC,12N)~OK EL=7OldeV/u
10
O
i
t
$
+
O
_2 o
=.
=,
*
10(
10
+
+L'
=k
*"
[13S+0.03] /*-,3+
'oF
',
÷I
I
÷
EL=?OMeV/u
÷
I
100
~'oCQ112C,12B)~OSc
+
O
J
/,o
I _2 °
i
_I o
i
0o
i
i°
i
2°
R
3°
I
~o
gem
Fiq. 9: A n g u l a r distributions of (12C, 12B) and (12C, 12N) reactions on 40Ca. We can f u r t h e r at small angles identify the population of 1 * states at 4.9 - 5.0 MeV and of a 6- state at ca. 6.0 MeV which shows up at larger angles. All strong transitions are of u n n a t u r a l parity. Most conspicous are the l o w lying states of unnatural parity (2~ 4~ 6") which are formed by the particle-hole c o n f i g u r a t i o n (sd)°s x (fp)l. They are observed in both charge exchange reactions and represent clean examples of angular momentum transfers L = 1 (2"), L = 3 (4") and L = 5 (6"). They can be well distinguished by their shapes of the differential cross sections (fig. 9). A strong enhancement of the cross section is observed in the excitation energy region from ca. 7 MeV up to 15 MeV for both reactions on 40Ca. They are actually m i r r o r reactions a p a r t f r o m the d i f f e r e n c e s in Q-values and t h e possible contributions of the 2 ÷ state of 12B*(0.95 MeV). Comparing the t w o spectra in fig. 10 and the t w o differences shown in the lower half of the spectra we can deduce the f o l l o w i n g result:
W. yon Oertzen / Excitation o f isovector modes
a)
369c
the strength in the region of 7 - 15 MeV is most likely the spinflip dipole resonance which is split into several states (Jn = O, 1, 2"). It is strongly populated in the angular range from 0° to 1° (®cm) which corresponds to assymptotic momentum transfers of 0.3 - 0.5 fm-1 and a corresponding angular momentum transfer 1-2 ft. The larger background in the (12C, 12B) spectra is attributed to an additional
b)
population of particle-hole states without spin-flip. Contributions due to three-body continuum (16)0 mainly due to pick-up and decay and knock-out are expected to be the same in both directions of charge exchange. c}
At larger excitation energies and at larger angles connected to large momentum transfers of ca. q > 0.65 fm-1, no distinctive structure is observed. The cross section in this region is dominated by large angular momentum transfers of L = 3 and more. The decreasing cross section reflects the Q-value dependence of the reaction.
I
300
H(12C.IZN)n
1oo
~ocn(12C,~N)LOK
!!
o=
:-
1oo
2.5°*_0.5° {H substr.)
200; 100
,.
.,.
,
.
,
,
,
,
. , . . . , . .
I,
200
=~ ~n
~'°Ca(~CflB)"°Sc i EL=7OHeV/u e,:o°:o.5o I~
I
I~
,....,....,..,,.
A=10°-2.5o)
,°°i
3OO2ooloo~'II,,A:10°-2"5°1 E~IMeV]
E,lMeV]
Fiq. 10:
Comparison of spectra of (12C, 12N) and (12C, 12B) reactions at small and large momentum transfer. The lower part shows differences of the spectra normalised in such a way that the spectra are similar at large Ex.
W. yon Oertzen / Excitation o f isovector modes
370c
b)
Resultsfor the 44Ca target
For a discussion of the results on the 44Ca nucleus we can refer to the (p,n) reactions studied on 48Ca (ref. 17). In the nucleus 44Ca (or 48Ca) unnatural parity states can be populated with the configurations [(f7/2)-1(f5/2)l]l+. and states formed by the remaining strength for protons in fp shell (f7/2, p3/2 and P1/2) giving states with spins of 3 +, 5 ÷ and 7 ÷.The angular distribution of the low lying 1 ÷ state (Gamov-Teller transition) shows a clear L = 0 angular distribution identical in shape with the corresponding transition on the 12C target (both shown in fig. 5). In fig. 1 1 we show a comparison of the "(p,n)" reactions on the two Ca-isotopes. The giant dipole strength is moved to higher excitation for the case of 44Ca and at low excitation energy strong transitions with low multipolarity are observed, e.g. Gamov Teller states, and isobaric analog states (both L = 0).
~Ca ( 12C
tt
12
200j
B)
~Sc
~
3
. l,
=
100 E ~o
o
~
20
2~
T
30
32
~0
¢5
5o
55
so
55
~-OCn(12C,12B)4-osc
300~200 100
1o
~
o
~
io
i~
zo
25
~o
3~
~o
ks
5o
~s
so
~
~0
Ex[ MeV] Fiq. 11:
Comparison of spectra of (12C, 12B) reactions on 40Ca and 44Ca.
In the "(n,p)" transitions on the two Ca isotopes (shown in fig. 12) we found a well concentrated group, which we attribute to the spin-flip dipole resonance. The low lying strength for 44Ca should contain the same transitions as in the case of the 40Ca target, which still have to be identified.
W. yon Oertzen / Excitation o f isovector modes
It will be quite difficult to search for L = 0 (Gamov Teller) transitions in the
3 71 c
"(n, p)"
direction because of the generally strong reaction yield on the hydrogen in the targets. The latter covers often the first few MeV in excitation energy.
H(12C,12N)n ~ Co.(12C,12N)l,l,K
il
ISO.
EL=7OMeVlu OL=O°+_0.5°
100
SO c
150
~°Co(12C,12N)('OK
-
0°+_0.5 100
50
• 10
.5
0
~
1Q
15
2o
~
30
~
~0
~
~
~
~
ExIMeV}
Fi.q. 12:
Comparison of spectra of (12C, 12N) reactions on 40Ca and 44Ca.
The shapes of the angular distributions have already been shown for some examples in figs. 5 and 9. from the empirical systematics of the shapes it appears possible to deduce angular momentum transfers, although preliminary calculations have not yet given satisfactory agreement with the data. The main difference occurs in the presence of a pronounced diffraction minimum in the region o f e c M = 2o-3°, in the calculations - which is not observed in the experiment. This problem seems of principal nature, because the shapes of the angular distributions are identical for the same angular momentum transfer on all target nuclei studied. Work on the theoretical analysis of these results is in progress (ref. 9).
372c
W. yon Oertzen / Excitation o f isovector modes
V.
REFERENCES
1)
H.B. Baer et al., Nucl. Phys. A396 (1983) 437c.
2)
A. Erell et al., Phys. Rev. C34 (1986) 1822.
3)
G.A. Needham et al., Nucl. Phys. A385 (1982) 349.
4)
M.C. Vetterli, O. H~usser et al., Phys. Rev. Lett. 59 (1987) 439.
5)
N. Anantaram et al., These Proceedings.
6)
W. yon Oertzen in "Frontiers in Nuclear Dynamics", ed. RA. Broglia and C.H. Dasso, P. 241-276 (1985).
7)
I. Meyer-ter-Vehn, Phys. Reports C74 (1981) 325.
8)
E. Oset, H Toki and W. Weise, Phys. Reports C83 (1982) 283.
9)
H.G. Bohlen, H. Lenske et al., to be published.
10)
W.A. Sterrenburg et al., Nucl. Phys. A 420 (1984) 257..
11)
A.C. Dodd, N.M. Clarke et al., J. Phys. G. 1~ (1985) 1035.
12)
W. yon Oertzen et al., Journal de Physique cC.44(1986) 175.
13)
D.E. Bainum etal., Phys. Rev. Lett. 44(1980) 1751.
14)
F. Osterfeld et al., Phys. Rev. C31 (1985) 372.
15)
T. Chittrakarn, 8. D. Anderson et al., Phys. Rev. C34 (1986) 80.
16)
E. Adamides et al., Nucl. Phys., in print.
17)
B.D. Anderson et al., Phys. Rev. C31 (1984) 147 and 1161.
357c
EXCITATION OF ISOVECTOR MODES IN HEAVY ION INDUCED CHARGE EXCHANGE REACTIONS*
W. von Oertzen Hahn-Meitner-lnstitut Berlin GmbH, 1000 Berlin 39, Germany and Fachbereich Physik, Freie Universit~t Berlin
Charge exchange reactions induced by 12C and 13C in the "(p,n)" and "(n,p)" direction have been studied in the energy range of 20 MeV/u to 70 MeV/u. The (12C, 12N) is particularly selective, it populates only (as = 1) spinflip states. The (13C, 13N) populates non spin-flip modes. Due to momentum transfers determined by Qvalues, the (12C, 12N) populates strongly Dipole transitions. Spin-flip Giant Resonances in 12C, 160, 40Ca, 44Ca and 58Ni are observed.
1. INTRODUCTION
Heavy ions offer a great variety of choices to induce charge exchange reactions which can be used to study isovector resonances in nuclei, Of particular importance are possibilities for the "(n,p)" transitions and double charge exchange which have so far been studied only in situations with rather strong experimental limitations namely induced by pions (1,2) and secondary neutron beams (3,4). We will focuss our attention to the light heavy ions, because they offer the best conditions with respect to experimental properties. We report here results of studies done with 12C and 13C projectiles at energies of 20 MeV/u up to 70 MeV/u. These results were obtained using magnetic spectrometers at the accelerator VlCKSI (HMI, Berlin), SARA (Grenoble) and GANIL (Caen).
Several questions can be addressed with these reactions: i) Evolution of the reaction mechanism as function of incident energy from two-step nucleon transfer to meson exchange. ii) Quantitative description of the cross-section in its dependence on momentum transfer.
Collaboration supported by PROCOPE:HMI/FU: H.G.Bohlen, E. Stiliaris,W. von Oertzen, S. Kubono; ISN, Grenoble: C. Berat, M. Buenerd, J.Y. Hostachy, Ph. Martin; CEN,Saclay:A. Miczaika (sup. by DFG),B. Fernandez,J. Barrette,B. Berthier;GANIL:W. Mittig 0375-9474/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
358c
HI. yon Oertzen / Excitation o f isovector modes
iii)
Selectivity for spinflip and non-spinflip transitions in relation to the GamovTeller and Fermi-transitions in nuclear p-decay.
iv)
Localisation and study of the properties of isovector "Giant" resonances with and without spinflip. We are only at the beginning of this venture and work from other laboratories is progressing along the same lines (5). Among the variety of choices of projectiles we will focus on the 12C and 13C nuclei. The most important property of the charge exchange reactions independent of the mechanism is the momentum transfer q due to the incoming and outgoing momenta ki and kf
-~ =-~-'~f.
(1)
We neglect the distortions due to the Coulomb and nuclear potentials and use the asymptotic values of the momenta in the initial (ki) and final (kf) channels. With this momentum transferred to the whole nucleus at the interaction radius Rint we obtain the preferential excitation of the multipole resonances with a multipolarity L, given by L= q
• Rint.
(2)
We have listed in table 1 the momentum transfer for different reactions and Qvalues at 70 MeV/u. The momentum transfer at 0° (it is minimum here) is given mainly by the Q-value, because there is no mass transfer in a direct charge exchange reaction: q = 0.11Q/x/-~-~
(3)
Here the incident energy per nucleon E/A and the Q-value are both in MeV and q is obtained in units of fm-1 In order to excite the modes with the lowest multipolarity we need the smallest Qvalues, or for given Q-values the highest possible incident velocity (in v'MeV/u). The variation of q with angle is of course very strong, if ki is large; typical variations of q with angle are given in table 1. The property described by equation 3, is common to all "inelastic" processes where no mass is transferred (6). A further important property which determines the reaction mechanism, is the momentum transfer in the quasi free reactions on a nucleon in the target which is given e.g. by the qvalues for p (12C, 12N)n as shown in table 1.
W. von Oer tzen / Excitation o f isovector modes
T a b l e 1.
The momentum transfers q using the assymptotic values of the m o m e n t a ki a n d k f a r e g i v e n f o r d i f f e r e n t reactions, reaction angles and Q-values.
~°Ca(12Cr 12NTI2B)
and 40Ca (13C~
a t EL:7OMeV/u Reaction Qo-values
q in [fm -l] 130 MeV/u
12 C
~Oca
~8Ca
90Z£
Qo[MeV]
-18,1
-30.7
-18.6
-29.3
-19.6
GO
0.25
0.41 0.45
0.24 0.38
0.39 0.49
0.26 0.42 O. 72
1°
Ex=10 HeY Go 1° 2o 5o
Qo[MeV] 0o
i° 2° 5o
Ex=lO MeV
~-
Go
v
1°
So Qo[Mev] GO lO° Ex=lO MeV •
13N) c e a c t i o n s
Target P
•
359c
0o 10°
O. 55
0.63
O. 72
0.29
1.02
1.48
1.56
1.70
-28,1
-40.7
-28.6
-39.3
-29.6
0.42
0.54 0.57 O. 66 1.08
0.38 0.48 0.70 1.50
0.52 0.60 O. 80 1.60
0.39 0.51 O. 77 1.72
0.44 -0.3
-15.6
-).5
-14.2
-4.5
O. 04 0.05 0.07 0.15
0.21 0.28 0.44 1.01
0.05 0.31 0.62 1.56
0.19 0.37 0.67 1.63
0.06 0.37 0.73 1.81
9Oz£
0.40 0.45 O. 59 1.16
0.61 0,64 O. 74 1.24
0.09 0.25 0.48 1.19
-13.0
-25.6
-13.5
-24.2
-14.5
0.18 0.18 0.19 0.22
0.34 O. 39
0.18 O. ]6
0.32 O. 45
0,19 O. 41
0.29 O. 37
0.52
0.65
0.72
0.73
0.55
1.04
1.56
1.65
1,81
1.21
_
0.0
-12.5
-0.53
-11.2
-1.50
0.00 0.08 0.16
0.17 0.22 0.33
0,01 0.15 0,31
0.15 0.21 0.33
0,02 0,16 0,31
-22.5
-10,5
-21.2
-11.5
0.33 0.35 0.42
0,14 0,20 0.33
0.30 0.34 0.41
0.16 0.22 0.34
The same kinematics holds for "(p, n ~" reaction given the same Q-values
0.03 0.11 0.21
0.26 0.27 0.32
360c
IV. yon Oertzen / Excitation o f &ovector modes
It is obvious from table 1 that for low multipolarities (L = 0, isovector monopol, and Gamov-Teller resonances), reactions like (p,n) or in,p) and also (t, 3He) as well as (13C, 13N) are well suited. We also find, that at the energies discussed here (20 MeV/u to 70 MeV/u) in the reactions involving 12C the L=0 resonances will be suppressed, because of the large momentum transfer q due to the Q-values incountered in the transitions. In addition to the considerations of the favoured multipolarity L, given by q • R, we have to consider the form factors in momentum space. Collectivity in nuclear states can be observed at low momentum transfer for 1" states due to the repulsive properties of the nucleon-nucleon interaction at small q. Collectivity can also be attained for states of low spin and unnatural parity (e.g. 2-) at high momentum transfer at typically twice the pion mass of ~ 2.3 fro-l, because of the attractive "properties of nucleon-nucleon interaction at large q (ref. 7,8). Form factors for 2" states (L= 1) may have large momentum components beyond the simple value of q given by q = L/R which for 40Ca is 0.2 fm-1 (R = 5 fm). For the collectivity at large momentum transfer of q ~ 2.3 fro-l, we have to face the problem of strong reduction of the cross section because of the scattering of the projectiles in the mean field of the target nucleus which decays fast with scattering angle (momentum transfer). In many experiments (VICKSI and GANIL) it was possible to make measurements around eL = 0 ° with the full solid angle of the magnetic spectrometer, the primary beam being stopped behind the first dipole at VlCKSl and GANIL The angular information was than obtained by the time of flight (VICKSI) or by ray tracing techniques (GANtL). Measurements around 0° turned out to be very important, not only in order to minimize the momentum transfer q, but also because the angular distributions show only in close vicinity to 0° characteristic differences for different multipolarities L.
II. PROPERTIES OF THE 12C A N D 13C INDUCED REACTIONS
a) Selectivity, reactions on 12Cand 160 A study of the (12C, 12N) and (13C, 13N) reactions at 30 MeV/u on the 12C and 160 targets showed an extreme difference in selectivity of final states (9). Fig. 1 shows two spectra of the two reactions on 12C at 30 MeV/u. We note the extreme difference in the population of final states. Fig. 2 shows a series of spectra of the (12C, 12N) reaction at 70 MeV/u. The two prominent peaks correspond to well
W. von Oertzen / Excitation o f isovector modes
361c
known states in 12B, the 1 + (ground state), and to the 2, 4°states at 4.37 MeV and 4.52 MeV (they are above the particle emission threshold). The structure observed at 7.8 MeV we attribute to the 1°state of the spin-dipole resonance which is mainly manifest in the 2- state at 4.4 MeV and possibly further strength (0- 1") at 10.3 MeV. The 1- state is quite narrow, its width of ~ 10 MeV is about 4 times the experimental resolution and is different from the 1- GDR observed in the case of (13C, 13N).
250
c3
~O C~
12C(12C,12N)12B
20C
Eiob = 358.4 MeV
15C
E)I:b = 3.4 o A® : 0 . 6 °
t C~ t
>
i Q_ i
10C 5C C 60C 50C
[=*b = 379.1 MeV ®~°== o , 0 o
~ _
~ ~'
I1 ~J
~-
40C 50C 200 100 0
16
12
8 E, [MeV]
4
0
Fi.q. 1 :Spectra of (12C, 12N) and (13C, 13N) reactions on 12C at 30 MeV/u. The systematic feature (in fig. 2) of the three states with decreasing cross section (4.37 MeV (2"), 7.8 MeV (1") and ca. 10 MeV (0")) suggests that the 2, 1, 0"members of the spinflip dipole are all observed; they have decreasing collectivity because of the possibilities to mix configurations, the absence of the broad structure due to the GDR which is observed in the (13C, 13N) case is rather remarkable. It shows that the GDR is not excited by a spinflip interaction. The dominance of the unnatural parity states in the case of (12C, 12N) is very large and we will assume that this conclusion is valid also for heavier targets (sect. III and IV).
W. yon Oertzen / Excitation of isovector modes
362c
t l
12C(12C,12N)12B EL=70HeV/u
0
10
20
30
40 -10 E,[MeV]
0
10
!
20
30
40
Fiq. 2: Spectra of (12C, 12N) reactions on 12C at 70 MeV/u.
2000 ~- I |
12C(12C12B)12N ELab=840MeV Qo=-30.70MeV
,
~ ~ ,
'~Lab=0.95°±0-16 °
300012C(I~J2N)128
lo
ELa~ 840,M~'V
20001
Qo40.70~V
.
"'~Lab=0.95%0-16°
L 0
5
10 15 20 Ex (MeV)
25
30
35
Fiq. 3: Comparison of (12C, 12N) and (12C, 12B) reactions on 12C at 70 MeV/u.
14I. yon Oertzen / Excitation o f isovector modes
363c
Comparing the (12C, 12N) and (12C, 12B) reactions in fig. 3 we find some differences, which we must attribute to the additional population of bound states in the case of the ejectile 12B. The two reactions populating the ground states of 12N and 12B are mirror reactions which must have the same cross sections. The additional structure observed at ca. 2.1 MeV excitation in the 12B spectrum indicates that the 2 ÷ states in both nuclei are excited ("mutual excitation"). This is suggested by the strong population of the 2 + state in the non spinflip reaction (13C, 13N) shown in fig. 1. The strong restrictive selectivity is lost in the (12C, 12B2+) branch and a larger class of states (as = 0 and as = 1) in the residual nucleus can be excited with considerable cross section, although this branch is smaller than the (12C, 12B1 + ) transition. This gives us some indication also to differences observed in the (12C, 12N) and (12C, 12B) spectra, in particular the continuum at higher excitation energies is more than a factor 2 higher in the case of 12B ejectiles (sect. IV).
105
_10 ~
i
102
101
10 0
-I0°
O'
0m
IO°-I0°
O°
0
10°
Fiq. 4: Angular distributions of transitions 12C(13C, 13N)12B at 30 MeV/u, the curves are one-step and two-step DWBA-calculations. The angular distribution for the most prominent transitions on the 12C-target are shown in figs. 4 and 5. In fig. 4 the left side shows calculations (ref. 9) at 30 MeV/u using the coupled reaction channel approach and two-step proton-neutron transfer. A very large space of configurations up to 2 he0 excitations had to be
364c
14/. yon Oertzen / Excitation o f isovector modes
included in order to obtain agreement with the data. The overall normalisation is given by the factor N2 and is in the range 4 to 10. The right hand side shows calculations with o~- direct charge exchange interaction without tensor interaction. There is a distinct difference in shape, which favours the assumption that at this energy the two-step transfer is strong and dominating for certain transitions at this energy. We notice that there is little oscillatory structure in the data at 70 MeV/u as opposed to the prediction of most simple one-step calculations. The unnatural parity states (spinflip states) are dominantly populated by the tensor interaction (10,11), and this may be the reason for the absence of diffraction structures. A characteristic feature, which shows dependence on the multipolarity, appears to be the position of the first maximum around 0° and thus the width of the angular peak around 0°
!
I
I
I
I
I
I
I
1000
1000
/ ~
[0.667÷0.77] *~
100
1=*,3+
L
~ 1000
+**
+,
÷
**
**
4'
"~100
[~.251 2, o
+ + '
$
+* * +
%0.
[1"7]'2+
lOO
$
10C
+
÷÷
[781
100(
++Ca112C,12BlU.Sc
+
Et:7OMeVlu 10(
\t
$
+
'i'
12C 1 (2C 12 'Z B lN l ~ EL=7OMeV uI i
' _; ° " o
°
. . 2. .0 . eCM
4o
+."
I
-2°-10
I
I
I
l
I
o°
1°
2°
3°
+0
eCM
Fig. 5: Same as Fig. 4 for 70 MeV/u for 12C and 44Ca targets. The curves are drawn to uide the eye. Note the similarity of the L=0 distributions for the t w o ifferent targets. Concerning the reaction mechanism the absolute prediction of cross sections needs further detailed work. Because of the internal momentum mismatch in transfer reactions for higher energies (6), we can expect that at energies of 50 to 70 MeV/u
IV. yon Oertzen / Excitation o f isovector modes
365c
the one-step charge exchange (meson exchange) dominates over the two-step transfer. III. (13C, 13N) AND (13C, 13B) REACTIONS AT 30 MEV/u The (13C, 13N) reaction should preferentially excite the non spinflip isovector modes. The most prominent one is the T> Giant Tipole Resonance (GDR) (L= 1), which is well observed at small angles (fig. 6). As already discussed with the results at 30 MeV/u (ref. 12) the (13C, 13B) reaction populates both spinflip (As = 1) and non spinflip (As = 0) transitions, however, the As = 1 transitions dominate. In both spectra shown in fig. 6 we see yield on top of a background beyond the GDR, which we interprete as the isovector quadrupol resonance.
p(13C,13N)n lZC(13C13N)lZB 2+{0.95MeV}
12C(13Co13B]lZN I EL=30MeVlUeL=IJ[8' *
60.0
I
300 -
I
1
2-,SFGDR{/,.2 HeY)
2
1*
.
200
300
/,00
pl
.
t, 100 CHANNELS
.
200
.
.
300
/,00
Fig. 6: (13C, 13N) and (13C, 13B) spectra on 12C target at 30 MeV/u. In fig. 7 we show spectra of the (13C, 13B) and (13C, 13N) reactions on 90Zr at 30 MeV/u. For the case of the "(p,n)" reaction we have used the results of previous work (13) and of calculations of Osterfeld (14) for the position of the resonances with multipotarity L=0, L= 1 and L= 2. With these assumptions we are able to describe the main intensity of the observed "bump" in the (13C, 13B) spectrum, with a remaining background, which we attribute to three body reactions. A similar attempt to fit was done for the (13C, 13N)) spectrum (fig. 7b). Fig. 7 also shows the differences between normalised spectra for both cases in order to emphasize the differences between spectra at small and at larger angles. We
366c
W. yon Oertzen / Excitation o f isovector modes
believe t h a t w i t h these differences the L = 1 and L = 2 strength is most likely singled out. The contributions from L = 0 are rather strongly suppressed as compared to (p,n) reactions due to the large m o m e n t u m transfers q as can easily be deduced f r o m table 1.
200
E~tM,vl .
90Nb
~ ~
+o '
9OZr(13 C 13B)9ONb 30MeV/u
eL:I.8°
Ioo
~
0
100
0m
,I ,4
PiI3C,I~N}~N~n r{
200 ~ ~
+
.
, ~ n
I00
~,,~" r'fl ll~jI
=. o
"~~00 g
.,.
100
~OZr(13C 13N)9O Y 30MeVlu
300
87
30 1~?~3,.+,s+~,o_
j
lO0~ 0 --
100
Fiq. 7aab:
'
+ 200 300 chcznnets
400
200
300 400 channels
(13C, 13B) and (13C, 13N) spectra on 90Zr at 30 MeV/u.
Vl. R E S U L T S F O R (12C, 12N) A N D (12C, 128) R E A C T I O N a t 7 0 M E V / u
In this chapter we show preliminary results of a study of "(n, p)" and "(p, n)" transitions studied at 70 MeV/u. The results on the targets 12C and 160 have shown t h a t the (12C, 12N) reaction produces d o m i n a n t l y final states w i t h As = 1 - t h a t is states w i t h unnatural parity n = (-)J ÷ 1 This feature enables us to discuss the results of reactions also for cases where the final states are not completely resolved.
a) 40Ca (12C, 12N or 12B) at 70 MeV/u These spectra were taken w i t h the spectrometer SPEG at GANIL w i t h an overall resolution of ~300 keV. A study of the 40Ca (p,n)40Sc (ref. 15) reaction at E = 134
367c
W. yon Oertzen/ Excitation of isovector modes
MeV allows us to identify the main low lying groups in the 40Ca (12C, 12B) reaction (fig. 8). The rather weak ground state group consists of a 3- and 4- state at 0.0 and 0.03 MeV; in our case we can identify this peak w i t h a L=3, As = 1 (J,, = 4 °) transition (d3/2 -~ f7/2). The d o m i n a n t peak in the spectrum consists of a 2- and 5state. We can assume t h a t it is characterised by L= 1, As = 1 (J,, = 2") transitions (d3/2 -. p3/2). The a n g u l a r d i s t r i b u t i o n s of these t w o groups clearly s h o w a difference which can be directly related to the momentum transfer (see table 1).
200 ,oo~ i
~
316°*-°160 =
I 2oo,I-
l
= 2oo~-
~
~°Cn(12C12B)~°Sc i EL:70~leV/u I e'--°32°-*°16° I
~
200
'~
200
20( )
;
0.63 °
'=
0.96°
I0C
o
6
. . . . . . . . . . . . . .
o
'. "~' ;; ' i'~ '
~
' ~
' *
' ~
' ~
'
~,
~ooto
I_
I
'
26°
1
6-
"
100
.......................................
~oo,L ' ;~::~.°
" ° " " ;.;/°"
E K [ MeV ]
Fiq. 8: Spectra of the (12C, 12N) and ,oo~- z ~ ~ _ . (12C, 12B) reactions on 40Ca . . . . . . . . . . . . . . . . .
"~--~
£,[MeVl
In fig. 9 w e show in addition the angular d i s t r i b u t i o n s of the c o r r e s p o n d i n g transitions in the (12C, 12N) reaction. For the case of an N = Z t a r g e t the t w o reactions should give identical results - because of charge symmetry. There is however, a difference in momentum transfer. The m o m e n t u m transfer of ca. 0.25 0.35 fm-1 at zero degrees suggests that the L = 1 angular distributions should give a maximum at 0 °. We actually observe a peak at almot 0 ° for the 2-transition,
368c
W. yon Oertzen / Excitation of isovector modes
w h e r e a s t h e group which we attribute to the 4-state shows a maximum at 1.0 °. At this angle the m o m e n t u m transfer is already 0.5 - 0.6 fm-1 ; w i t h a nuclear radius of ca. R = 5 fm we clearly obtain o p t i m u m conditions from q • R for L = 3. We notice a difference in the shape of the group at 0.9 MeV excitation, which in the case of (12C, 12N) is a pure 2"state, and in the case of (12C, 12B) contains the 12B2+ transition w i t h an angular m o m e n t u m transfer of L = 3. I
I
I
I
I
I
I
[GS.0.03]
~-,3100 <'÷
' Ii'
t
,~,÷ +
O
**
I
,
[0.7/,.0.891 =2-,5-
O
[0.7/*,0.891
2__-,5-
100
O
i
_i °
i
J
0o
i°
ecM
i
2°
i
3°
~OCo(lZC,12N)~OK EL=7OldeV/u
10
O
i
t
$
+
O
_2 o
=.
=,
*
10(
10
+
+L'
=k
*"
[13S+0.03] /*-,3+
'oF
',
÷I
I
÷
EL=?OMeV/u
÷
I
100
~'oCQ112C,12B)~OSc
+
O
J
/,o
I _2 °
i
_I o
i
0o
i
i°
i
2°
R
3°
I
~o
gem
Fiq. 9: A n g u l a r distributions of (12C, 12B) and (12C, 12N) reactions on 40Ca. We can f u r t h e r at small angles identify the population of 1 * states at 4.9 - 5.0 MeV and of a 6- state at ca. 6.0 MeV which shows up at larger angles. All strong transitions are of u n n a t u r a l parity. Most conspicous are the l o w lying states of unnatural parity (2~ 4~ 6") which are formed by the particle-hole c o n f i g u r a t i o n (sd)°s x (fp)l. They are observed in both charge exchange reactions and represent clean examples of angular momentum transfers L = 1 (2"), L = 3 (4") and L = 5 (6"). They can be well distinguished by their shapes of the differential cross sections (fig. 9). A strong enhancement of the cross section is observed in the excitation energy region from ca. 7 MeV up to 15 MeV for both reactions on 40Ca. They are actually m i r r o r reactions a p a r t f r o m the d i f f e r e n c e s in Q-values and t h e possible contributions of the 2 ÷ state of 12B*(0.95 MeV). Comparing the t w o spectra in fig. 10 and the t w o differences shown in the lower half of the spectra we can deduce the f o l l o w i n g result:
W. yon Oertzen / Excitation o f isovector modes
a)
369c
the strength in the region of 7 - 15 MeV is most likely the spinflip dipole resonance which is split into several states (Jn = O, 1, 2"). It is strongly populated in the angular range from 0° to 1° (®cm) which corresponds to assymptotic momentum transfers of 0.3 - 0.5 fm-1 and a corresponding angular momentum transfer 1-2 ft. The larger background in the (12C, 12B) spectra is attributed to an additional
b)
population of particle-hole states without spin-flip. Contributions due to three-body continuum (16)0 mainly due to pick-up and decay and knock-out are expected to be the same in both directions of charge exchange. c}
At larger excitation energies and at larger angles connected to large momentum transfers of ca. q > 0.65 fm-1, no distinctive structure is observed. The cross section in this region is dominated by large angular momentum transfers of L = 3 and more. The decreasing cross section reflects the Q-value dependence of the reaction.
I
300
H(12C.IZN)n
1oo
~ocn(12C,~N)LOK
!!
o=
:-
1oo
2.5°*_0.5° {H substr.)
200; 100
,.
.,.
,
.
,
,
,
,
. , . . . , . .
I,
200
=~ ~n
~'°Ca(~CflB)"°Sc i EL=7OHeV/u e,:o°:o.5o I~
I
I~
,....,....,..,,.
A=10°-2.5o)
,°°i
3OO2ooloo~'II,,A:10°-2"5°1 E~IMeV]
E,lMeV]
Fiq. 10:
Comparison of spectra of (12C, 12N) and (12C, 12B) reactions at small and large momentum transfer. The lower part shows differences of the spectra normalised in such a way that the spectra are similar at large Ex.
W. yon Oertzen / Excitation o f isovector modes
370c
b)
Resultsfor the 44Ca target
For a discussion of the results on the 44Ca nucleus we can refer to the (p,n) reactions studied on 48Ca (ref. 17). In the nucleus 44Ca (or 48Ca) unnatural parity states can be populated with the configurations [(f7/2)-1(f5/2)l]l+. and states formed by the remaining strength for protons in fp shell (f7/2, p3/2 and P1/2) giving states with spins of 3 +, 5 ÷ and 7 ÷.The angular distribution of the low lying 1 ÷ state (Gamov-Teller transition) shows a clear L = 0 angular distribution identical in shape with the corresponding transition on the 12C target (both shown in fig. 5). In fig. 1 1 we show a comparison of the "(p,n)" reactions on the two Ca-isotopes. The giant dipole strength is moved to higher excitation for the case of 44Ca and at low excitation energy strong transitions with low multipolarity are observed, e.g. Gamov Teller states, and isobaric analog states (both L = 0).
~Ca ( 12C
tt
12
200j
B)
~Sc
~
3
. l,
=
100 E ~o
o
~
20
2~
T
30
32
~0
¢5
5o
55
so
55
~-OCn(12C,12B)4-osc
300~200 100
1o
~
o
~
io
i~
zo
25
~o
3~
~o
ks
5o
~s
so
~
~0
Ex[ MeV] Fiq. 11:
Comparison of spectra of (12C, 12B) reactions on 40Ca and 44Ca.
In the "(n,p)" transitions on the two Ca isotopes (shown in fig. 12) we found a well concentrated group, which we attribute to the spin-flip dipole resonance. The low lying strength for 44Ca should contain the same transitions as in the case of the 40Ca target, which still have to be identified.
W. yon Oertzen / Excitation o f isovector modes
It will be quite difficult to search for L = 0 (Gamov Teller) transitions in the
3 71 c
"(n, p)"
direction because of the generally strong reaction yield on the hydrogen in the targets. The latter covers often the first few MeV in excitation energy.
H(12C,12N)n ~ Co.(12C,12N)l,l,K
il
ISO.
EL=7OMeVlu OL=O°+_0.5°
100
SO c
150
~°Co(12C,12N)('OK
-
0°+_0.5 100
50
• 10
.5
0
~
1Q
15
2o
~
30
~
~0
~
~
~
~
ExIMeV}
Fi.q. 12:
Comparison of spectra of (12C, 12N) reactions on 40Ca and 44Ca.
The shapes of the angular distributions have already been shown for some examples in figs. 5 and 9. from the empirical systematics of the shapes it appears possible to deduce angular momentum transfers, although preliminary calculations have not yet given satisfactory agreement with the data. The main difference occurs in the presence of a pronounced diffraction minimum in the region o f e c M = 2o-3°, in the calculations - which is not observed in the experiment. This problem seems of principal nature, because the shapes of the angular distributions are identical for the same angular momentum transfer on all target nuclei studied. Work on the theoretical analysis of these results is in progress (ref. 9).
372c
W. yon Oertzen / Excitation o f isovector modes
V.
REFERENCES
1)
H.B. Baer et al., Nucl. Phys. A396 (1983) 437c.
2)
A. Erell et al., Phys. Rev. C34 (1986) 1822.
3)
G.A. Needham et al., Nucl. Phys. A385 (1982) 349.
4)
M.C. Vetterli, O. H~usser et al., Phys. Rev. Lett. 59 (1987) 439.
5)
N. Anantaram et al., These Proceedings.
6)
W. yon Oertzen in "Frontiers in Nuclear Dynamics", ed. RA. Broglia and C.H. Dasso, P. 241-276 (1985).
7)
I. Meyer-ter-Vehn, Phys. Reports C74 (1981) 325.
8)
E. Oset, H Toki and W. Weise, Phys. Reports C83 (1982) 283.
9)
H.G. Bohlen, H. Lenske et al., to be published.
10)
W.A. Sterrenburg et al., Nucl. Phys. A 420 (1984) 257..
11)
A.C. Dodd, N.M. Clarke et al., J. Phys. G. 1~ (1985) 1035.
12)
W. yon Oertzen et al., Journal de Physique cC.44(1986) 175.
13)
D.E. Bainum etal., Phys. Rev. Lett. 44(1980) 1751.
14)
F. Osterfeld et al., Phys. Rev. C31 (1985) 372.
15)
T. Chittrakarn, 8. D. Anderson et al., Phys. Rev. C34 (1986) 80.
16)
E. Adamides et al., Nucl. Phys., in print.
17)
B.D. Anderson et al., Phys. Rev. C31 (1984) 147 and 1161.