The (p, n) reaction on cadmium isotopes leading to the ground- and excited-state analogs

Nuclear Physics A377 (1982) 163-175 © North-Holland Publishing Company

THE (p, n) REACTION ON CADMIUM ISOTOPES LEADING TO THE GROUND- AND EXCITED~STATE ANALOGS T. MURAKAMI, S. NISHIHARA, T. NAKAGAWA and S. MORTTA f

Department of Physics, Facwlty of Science, Tohoku University, Sendai 980, Japan H. ORIHARA

Cyclotron and Radioisotope Center, Tohoku University, Sendai 980, Japan K. MAEDA College of Genera! Education, Tohoku University, Sendai 980, Japan and K. MIURA Tohoku Institute of Technology, Nagamachi-Koeji, Sendai 982, Japan Received I1 September 1981 A6®tract : The (P, n) reactions to ground- and excited-state analogs on "°" "a" "6Cd have been studied at a bombarding energy of 25 MeV. Angular distributions of emitted neutrons leading to ground-state analogs, and 2+, 3- and4+ excited-stateanalogs were obtained for each target. Angulardistributions of differential sass suctions to the ground-state analog agree with the predictions obtained from maaoscopic DWBA calculations in which a Lane potential is employed. Coupled-channel calculations indicate the importance of two-step processes in the (p, n) transition to an excited-state analog. Further, the calculation using a larger value for the deformation parameter of the isovector part than of the isoscalar one fairly well describes the 2+ excited-state analog . E

NUCLEAR REACTIONS "° " "a " "° Cd(p, n), E = 25 .0 MeV. "° " "' " " 6In deduced isobaric analog states, J, rz . Enriched targets.

1. Introduction In experimental studies of charge-exchange reactions, analog states corresponding to both ground and low-lying excited states in the target nucleus are prominent features ofthe spectra; namely, ground-state (GSA) and excited-state (ESA) analogs. Satchler, Drisko and Bassel t) made a DWBA calculation of the (p,n) reaction to the ESA, employing a deformed Lane potential as the interaction responsible for the transition . Their calculation gave cross sections smaller than observed ones by t Present address ; Research Conter of Ion Beam Technology, Hosei University, Koganei, Toryo 184, Japan. 163

164

T. Murakaml et at. / Ttee (p, n) reaction

more than an order of magnitude. Madsen et al. Z ) pointed out that the two-step processes, namely the (p, p') transition followed by the quasielastic charge-exchange transition and the quasielastic charge-exchange transition followed liy the (n, n') transition, might be of essential importance for the (p, n) reaction leading to the ESA. They have performed a coupled-channel calculation and successfully reproduced experimental cross sections for the (p, n) reactions on 26 Mg and S 6 Fe leading to the ESA. The same conclusions have also been obtained from the studies on even molybdenum 3) and samarium a) isotopes at Ep = 16-26 MeV. In this paper, we present the experimental results of the (p, n) reactions on t t o, t t a, . 't6Cd leading to the GSA and ESA, and the analyses of them in which the two-step transitions to the ESA are taken into account. Further, the isospin dependence of the deformation parameter is presented. Sect. 2 describes the experimental procedure and data reduction. The results are shown in sect. 3. The comparison of them with the calculated values is discussed in sect . 4, and sect. 5 presents a summary. 2. Experimental procedure A 25 MeV proton beam was obtained from the AVF cyclotron at the Cyclotron and Radioisotope Center, Tohoku University, and emitted neutron energies were measured by the time-of-flight method. The frequency of the cyclotron RF was so high (32 MHz) for time-of-flight spectroscopy in the energy range of interest here that two external beam choppers were used to reduce the beam pulse repetition rate by a factor of 12. The flight path was 24.6 m. Angular distributions of emitted cWnl ®a~~.

TIrEI

r~®~

w®

®~® ®'

W

~~®

TeF

rhum

m~.®~.~

nilel Ir:TEr

û~

~®

rE~cer

m_ .®~,®

Fig. l . Electronic set-up used for time-of-flight measurements. Usually, two systems with two neutron detectors and with the eight ADC's are used at once.

T. Murakami et al. / The (p, n) reaction

165

neutrons between 0° and 145° were obtained by employing a beam swinger system, which consisted of three dipole magnets. Two of them rotate around the axis on which a target is placed, andhence the angle of a proton beam relative to the direction of detectors can be changed. The detectors are NE2131iquid scintillators contained in the cells made of Pyrex glass, which have dimensions of 50 x 10 x 5 ctn 3 and 50 x 10 x 7.5 cm 3 . Two photomultipliers were attached to both ends of the long axis in each detector, and neutrons are irradiated from the direction perpendicular to the long axis . Four kinds of data were stored on magnetic tape through a data acquisition system : (i) time offlight, (ü) position in the detector where the scintillation was generated, (iii) pulse shape data for neutron-gamma discrimination and (iv) summed light output . The block diagram of the electronic circuits is shown in fig. 1 . The time~f--flight data are compensated for the light transmission time in the detector, then gated by n-y discrimination and light output data . Because the counting rate of the beamindependent backgrounds is very high in such a large-volume detector, the n-y discrimination is an important technique in detecting the neutrons. The property of the n-y discrimination versus the light output is demonstrated in fig. 2.

IEITIII " 11~~1-IIiC11~lI1T111

Fig. 2. Two-dimensional display of the n-y discrimination versus the pulse height of summed light output when natural lithium was bombarded by 24.5 MeV protons. Time per channel (n-y. discrimination) is 0 .8 ns and energy per channel (light output) is 1 .1 MeV. TABLE 1

Isotopic composition (in ~) and thickness (in mg/cm2) of cadmium targets Target iio~ i i a Cd ~ie~

Mass 106

108

110

111

Thickness

112

113

114

116

0.10

0 .09

96 .00

1 .55

1 .10

0 .36

0.63

0 .16

4.75

< 0.01

< 0 .01

0 .08

0 .19

0.40

0 .60

98 .55

0 .19

4 .98

0.06

0 .02

0 .31

0.35

0.86

0 .47

1 .41

96 .53

5 .32

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T. Murakami et al. / The (p, n) reaction

The detection efficiency of the detector was determined by using the'Li(p, n)'Be reaction at 6 S Ev S 35 MeV. Neutron yields from this reaction were normalized to the absolute cross sections which have been reported by Poppe et al. ') and Schery et al. 6 ) . More complete discussion of experimental techniques and detector efficiencies are given in ref. '). The targets were prepared by rolling isotopically enriched cadmium metals, and their thickness was estimated by weighing . The isotopic composition and the thickness for each target are tabulated in table 1. 3. Experimental results

Fig. 3a shows an energy spectrum of neutrons from the ' t °Cd(p, n) t t o In reaction observed at 60° relative to the direction of the proton beam. The abscissa corresponds to the neutron energy translated from the time of flight, and each bin width is 50 keV. The time resolution is about 1 .4 ns and it corresponds to 120 keV of energy resolution in the GSA region . The ordinate is compensated for the variation of detection efficiency which depends on the neutron energy . To avoid overlap of the low-energy neutrons with the high-energy neutrons from a later burst, an appropriate detector bias (say E~ = 2.4 MeV in this case) is employed. In this spectrum the GSA and some ESA are seen to be excited. The excitation energies ofthe GSA and relative energies ofthe ESA with respect to the GSA obtained Ilocd fp,nl IIOIn Ep "25 MTV slab. " 60 "

c~

Fig . 3a . Energy spectrum of neutrons from the "°Cd(p, n)"oIn reaction obtained from the time-of-flight measurement at a bombarding energy of 25 MeV and a flight path of ?A.6 m. The ordinate is compensated for the variation of detector efficiency. The dashed curve is an assumed background to the individual peaks of the analog states .

T. Mwakami et al. / The (p, n) reaction

167

114Cd (p,n)II~In Ep "23 MeV elab."60 "

z 0 U

Fig. 3b . Same as fig. 3a but for the

"aCd(p, n)"`In

reaction .

116 Cd (p,n) IIS In Ep "25 MeV elob.' 60 "

600 N H z V

300

s

io

~s NEUTRON ENERGY (MeV1

Fig. 3c . Same as fig. 3a but for the

za

"6Cd(p, n)" 6In reaction .

in the present experiment are listed in table 2, where the Coulomb displacement energies from ref. s) are also given for comparison. The spins and parities given in this table are those of the parent states . The FSA corresponding to the 2+, 3 - and 4+ vibrational states in parent nuclei were observed in all of the (p, n) reactions on t ~ oCd, t t °Cd and tt6Cd. (See also figs . 3b, c.) In every case, the relative energy of

T. Murakami et al. / The (p, nJ reaction

168

TAHLE 2 Levels presently observed by the (p, n) reactions on cadmium isotopes Target

J*

Energy')

~io~

0* 2* 34* (0*, 2*, 4*)

13 .4910.05 0.67 2.09 2.3 1 .5

Ref. e)

1 .8

2.5 2.7 3.0 "`Cd

iie~

0* 2* 34* (0*, 2*, 4*) 0*

2* 34* (0*, 2*, 4*)

13 .3310.05 0.56 1 .97 2.38 1.3 2.8

13 .310±0.015

13 .2410.05 0.50 1.90 2.42 1 .3 2.7

') Values for the 0* GSA are the Coulomb displacement energies, and those for the ESA are the energies relative to the GSA.

the ESA with respect to the GSA is in good agreement with the excitation energy of the parent state. Fig. 4 shows angular distributions of neutrons leading to the GSA. The curves in the figure are the theoretical results and will be fully described in sect. 4. The angular distributions were obtained by assuming continuous backgrounds represented by quadratic functions, and they are shown by dashed curves in figs. 3a-c. Error bars attached to the experimental points stand for statistical uncertainties. An absolute error in a differential crcsss section is estimated to be within 20 ~, which comes mainly from the errors in determination of the detector efficiency and the target thickness. Figs . 5-7 show the angular distributions to the 2*, 3 - and 4+ ESA, respectively. It is worth noticing that the angular distributions to the 2 * ESA on three kinds of isotopes are similar to one another and exhibited the larger cross sections at forward angles rather than backward angles in all targets presently studied.

T. Mwakami et al. / The (p, n) reaction

169

Fig. 4. Angular distributions forthe 0 + GSA. Theerror bars stand for statisticaluncertainties. Thecurves are the cross sections calculated with three different parameter sets in the Lane potential.

4. Calculated results and discussions 4.1 . 0 + GROUND-STATE ANALOG

It is well known that the Lane potential 9) can successfully reproduce the cross section for the (p, n) reaction leading to a GSA. By using the computer code DWUCK [ref. 1°)] we have estimated the 0+ GSA cross section. Measured cross sections have been compared with the predictiôn. In the Lane model the optical potential has the form like,

l ~o

T. Murakami et al. / The (p, n) reaction

w a _E v w b v

Fig . Sa . Angular distribution for the "'Cd(p,n)' `4In transition to the 2* E5A. The curves are theoretically predictedaoss sections by calculations (a) (dot~ashed line), (b) (solid line) and (c) (dashed line).

Fig. Sb . Angular distributions for the (p, n) transitions to the 2* ESA in "°' "'" "bln. The curves are predictedcross sections by calculations (b) (solid line) and (c') (dashed line), which are multiplied by a factor of 0.8 . The experimental values of the "~Cd(p, n)"`In reaction are the same as thoseof fig. 5. The ratio of~i'/~i' used in the calculation (c) are 2, 3 and 4 for the reactions on "°Cd, "`Cd and "6Cd, respectively.

T. Murakami et al. / The (p, n) reaction ACd(p,n)AIn

ACd(p,n)Aln

" Exp. - 2step + Direct --- Direct

" Exp. -2 step

Ep " 25 MeV 3-

Ex " 2.09 MeV f

Ep " 25 MeV 4+

Ex " 2.3 MeV

A " I10

If

N E v \ b v

Fig. 6. Angular distributions for the (P, n) transitions to the 3- ESA in "° " "`" "6 In . The curves show the results of the calculation (c) (solid line), whicharemultiplied by a factor of 2 to the calculated results and (a) (dot~ashed line), which is multiplied by a factor of 50 .

Fig. 7. Angular distributions for the (p, n) transitions to the 4+ ESA in "°~' ", "6 In. The solid lines show the results of the calculation (b), which are multiplied by a factor of 3.

where superscripts (0) and (1) mean the isoscalar and isovector part, respectively . The calculations were carried out with three kinds of parameter sets for U(r) . Results are shown in fig. 4 together with experimental values ; the dot-dashed curve is obtained with optical-model parameters given by Beochetti et al . tt ) (Pl), the solid curve is calculated with those given by Carlson et al. t2) (P2), and the dashed curve by Patterson et al. ts) (P3) . In the parameter sets labeled by Pl and P2, the opticalmodel parameters for neutrons were obtained by reversing the sign of a symmetry term oo (N-~ from the parameter set for the proton . In the calculations of the

172

T. Mwakmrri et d. / The (p, n) reaction

tto~(p~ n)ttoIn and tts~(p~ n)ttsIn reactions we have used the distorted waves which were made from the potentials of t '4Cd and tt4In, because it was plausible that the optical potentials for the present three isotopes were quite alike. The magnitude and shape of differential cross sections were reproduced by these calculations. Especially, they were well fitted by the calculation with parameter set P2.

â _E

b 5

QS

L0 L~ (N-Zl/A= x 10

Fig. 8 . Cross sections of the (p, n) transition to the 0 + ground-state analogs integrated from 0° to 120° . The experimental value on s 6 Fe has been obtained in this laboratory [see ref. ")] . The values on molybdenum and samarium isotopes are quoted from refs.' `). The dashed line is the result obtained by a least square fitting to the experimental values except those on samarium isotopes.

The observed cross sections integrated from 0° to 120° seem to vary proportional to (N-~lAa as shown in fig. 8. These results suggest that the Lane model is a good description for the transition to the GSA at this incident energy and for these target nuclei . 4.2. 2 + EXCITED-STATE ANALOG

In this report three sorts of calculation are presented for the (p, n) transition to the 2 + ESA which corresponds to the one-phonon 2+ state in the target nucleus : (a) a DWBA calculation carried out by taking account of the direct transition only; (b) a coupled-channel calculation taking account of the two-step processes, i.e. (i) the quasielastic transition to the GSA followed by the transition to the 2+ ESA and (ü) the transition to the one-phonon 2+,excited state ofthe target nucleus followed by the quasielastic transition to the 2+ ESA ; (c) a coupled-channel calculation done by taking account of the two two-step transitions and the direct transition . The calculations have been made within the frame work of a macroscopic calculation, by using the code CHUCK t`) . The ground state, the one-phonon state of the target nucleus and their analogs were included in calculations (b) and (c).

T Murakami et al. / The (p, n) reaction

173

The interacting potential of the form T U - -~R .d ßZo)Uco)+ßZ1~U~1~t . drl A l'

(2)

is assumed in these calculations, where ß2 ° ~ and ßZ 1 ' are the deformation parameters . We have carried out the calculation with set P2 for U°~ and Ü(1) . The depth of the imaginary part of the optical potentials, however, was multiplied by a factor of 0.8, in order to account for the explicit inclusion of the 2 + state in the coupled-channel calculation. Then the cross section of the 0 + GSA calculated by the code CHUCK should be the same as that obtained with DWUCK. The dash-dot curve in fig. Sa is the result of the calculation (a), which is multiplied by a factor of 50, with ß2 l) equal to the experimental ßZ. The value of ßZ was taken from the literature 1 S), obtained from a Coulomb excitation experiment . The solid curve in fig. Sa is the cross section obtained from the calculation (b), with ß2° ~ equal to ßZ" The dashed curve in fig. Sa is the result of the calculation (c). For simplicity, both ß2 °1 were taken to be equal to ßZ . The calculations (b) and (c) roughly reproduced the observed cross section at B~.m. - 0°. But it should not be ignored that calculated differential cross sections overestimate so much at the angles from 20° through 50°. 4.3 . MAGNITUDE OF fz'

As pointed out by Madsen et al. 16), in general ß2 °' and ßZ 1 ' in eq . (2) are different to each other. The ratio of ~Z 1)/ß2°~ was estimated to be about 1 .7 for 12°Sn with "no parameter schematic model" . Recently we have reported l') the 56 Fe(p, n)' 6 Co reaction leading to the anolog states of the ground and the first excited 2 + state in s 6 Fe which has been studied at Ep = 20, 28, 32 and 35 MeV. Direct process dominated at higher energies, and thus the direct extraction of the isovector deformation parameter ~z ~ was feasible . It was found that ~i ~ was about three times larger than ~°l z . The cross section of the (p, n) reaction leading to an ESA has been expected to strongly depend on the value of FiZ I) . The two-step mechanism is dominant in the (p, n) reaction to the ESA at Ep = 25 MeV. But the discrepancy of the measured differential cross sections from calculated ones has suggested that {'Z1) gives an important effect through the interference between the one- and two-step transitions. Hence the calculation in which the ratio of ßZ1 )/ß2 ° ' was not unity was carved out [c')] . The dashed curves in fig. Sb represent the cross sections obtained from the calculations (c') in which ~i~ is tentatively taken to be equal to ßZ, and ~i ~ equal to 2ßZ, 3ß z and 4ß Z for the reactions on 11o Cd, llama and 116Cd, respectively . The calculated results in fig. Sb are multiplied by a factor of 0 .8 . The angular distributions agree with the dashed curves [calculation (c')] which are better than solid ones

17 4

T. Murakami et al. / Tke (p, n) reaction

Integrated cross sections

calculation (a) calculation (b) calculation (c') . experiment °)

of the 2+

TABLE 3 ESA obtained by calculations and experiments (in mb)

' `°Cd

"°Cd

" 6Cd

(1 .00)') 1 .98 (I .00) 1 .66 (1 .00) 1 .23 (I .00)

(1 .33) 2.60 (1 .31) 2.05 (1 .24) 1.41 (I .15)

(1 .55) 2.98 (1 .51) 2.27 (1 .37) 1 .45 (1 .18)

') The values in the parentheses are the ratios relative to those of "°Cd . b) The values of experimental cross section were obtained by integrating the differential cross sections from 0° through l20° .

[calculation (c)]. It should be noticed in table 3 that the relative yields of t 14Cd and 'tsCd to that of't oCd are well explained by estimation in which ß2t 1 is equal to 2ßZ, 3ßZ and 4ß Z for t t o Cd, t tam and t t 6 Cd, respectively . It also affects the inelastic scattering meâsurement that the ß2t1 is not equal to ß2 °~. The differential cross sections of protons which inelastically excite the first 2 + state are different from those of neutrons. Recently precise date of inelastically scattered neutrons have been reported t e. t 9 . Their analyses for the (n, n') experiments to the first 2+ state on tin isotopes with a macroscopic model were compared with those of (p, p') or Coulomb excitation, and it was found that the ß2 t1/NZ ° ~ ratios lay around 2. These values are consistent with those obtained from the present (p, n) experiments on cadmium isotopes . 4.4 . 3 - AND 4+ EXCITED-STATE ANALOG

Assignment for the 3 - and 4 + ESA is rather ambiguous since the one-phonon 3 - and 4 + states are not well established in the parent nuclei . For the 3 - and 4+ ESA, the calculations of the same type as for the 2+ ESA have been tamed out. In calculations (b) and (c) the depth of the imaginary part of the optical potential for the 3 ESA was multiplied by a factor of 0.9, while the same value as in the DWBA calculation was used for the 4+ ESA. The dash-dot curve in fig. 6 is the result of the calculation (a) for the 3 - state which is multiplied by a factor of 50 . The solid curves are the cross sections obtained from the calculation (c) with ß3° ~ and ß3t 1 which are equal to the experimental ß3 . The calculated cross sections are multiplied by a factor of 2 . In fig. 7a comparison with the calculation (b), in which ~a °i is equal to experimental ßa, is shown by a solid curve . Note that the calculated value i multiplied by a factor of 3 . The calculation (a) for the 4 + ESA gives cross sections 50 times smaller in magnitude than experimental cross sections, as in the case of the 3 - ESA. The "experimental" ßs and ßa mentioned above were quoted from the (p, p') study at EP = 52 MeV [ref. z°)] .

T. Murakami et al. / The (p, n) reaction

17 5

5. Summary Measurements and coupled-channel analyses for the (p, n) reaction to the analog states in the cadmium isotopes (A = 110, 114 and 116) have been presented. The analog states of the 2+, 3 - and 4 + one-phonon states were observed for all targets. Relative energies of these excited-state analogs with respect to the 0+ ground-state analogs are in good agreement with the excitation energies of the parent states . The measured cross sections of the 0 + states grow proportionally to (N-~lAs . The angular distributions are well reproduced by the DWBA calculation using the Lane potential. Thus it is suggested that the Lane potential is a fairly good description of these (p, n) reactions to the 0+ ground-state analogs. The coupled-channel analyses show the importance of the two-step processes in the (p, n) transition to the ESA ; the cross sections calculated by assuming only the direct transition are about 50 times smaller than the observed cross sections, while the coupled-channel calculations taking the two-step process into account reproduce the observed cross sections. Furthermore it is also noted for the 2 + ESA that the coupled~hannel calculations taking account of the direct transitions, as well as the two-step transitions with ßZ'1 ~ ßZ °l , best explain the observed cross sections. The authors are indebted to Messrs . K. Hoshika, H . Ohmura, H . Ono, S. Kan and Y. Saiki for helpful operation of the cyclotron. References 1) G. R. Satchler, R. M. Drisko and R. H. Bassel, Phys. Rev. 136 (1964) B637 2) V. A. Madsen, M. J. Stomp, V. R. Brown, J. D. Anderson, L. Hansen, C. Wong and J. J. Wesolowski, Phys . Rev. Lett. 28 (1972) 629 3) V. A. Madsen, V. R. Brown, S. M. Grimes, C. H.Puppe, J. D. Anderson, J. C. Davis and C. Wong, Phys . Rev. C13 (1976) 548 4) C. Wong, V. R. Brown, V. A. Madsen and S. M. Grimes, Phys. Rev. C20 (1979) 59 5) C. H. Puppe, J. D. Anderson, J. C. Davis, S. M. Grimes and C. Wong, Phys. Rev. C14 (1976) 438 6) S. D. Schery, L. E. Young, R. R. Doering, S. M. Austin and R. K. Bhowmik, Nucl . Instr.147 (1977) 399 7) H. Orihara and T. Murakami, Nucl . Instr. 188 (1981) 15 8) M. Harchol, A. A. Jaffe, J. Miron, I. Unna and J. Zioni, Nucl. Phys . A90 (1967) 459 9) A. M. Lane; Phys . Rev. Lett. 8 (1962) 171 ; Nucl . Phys. 35 (1962) 676 10) P. D. Kunz, private comununication 11) F. D. Becchetti, Jr . and G. W. Greenlees, Phys. Rev. 192 (1969) 1190 12) J. D. Carlson, C. D. Zafiratos and D. A. Lind, Nucl. Phys. A249 (1975) 29 13) D. M. Patterson, R. R. Doering and A. Galonsky, Nucl . Phys. A263 (1976) 261 14) P. D. Kunz,,privatecommtmication 15) P. H. Stelson and L. Grodzins, Nucl . Data Al (1965) 21 16) V. A. Madsen, V. R. Brown andJ . D. Anderson, Phys. Rev. C12 (1975) 1205 17) H. Orihara, T. Murakami, S. Nishihara, T. Nakagawa, K. Maeda, K. Miura and H. Ohnuma, Phys. Lett. 106B (1981) 171 18) R. W. Finlay,J. Rapaport, M. H. Hadizadeh, M. Miriea and D. E. Bainum, Nucl. Phys. A338 (1980) 45 19) D. E. Bainum, R. W. Finlay, J. Rapaport, M. H. Hadizadeh, J. D. Carlson and J. R. Comfort, Nucl . Phys. A311 (1978) 492 20) M. Koike, I. Nonaka, J. Kokame, H. Kamitsubo, Y. Awaya, T. Wada and H. Nakamura, Nucl . Phys . A12S (1969) 161