Extension of “complete spectroscopy” to charged-particle fusion reactions

Physics Letters B 320 (1994) 7-11 North-Holland

PHYSIC S LETTERS B

Extension of "complete spectroscopy" to charged-particle fusion reactions Jean Kern PhystcsDepartment, Universttyof Fnbourg, CH-1700Fnbourg, Swttzerland Received 1 June 1993; revised manuscript received 2 November 1993 Echtor: R.H. Siemssen

Reactions that provide "completespectroscopy"are very important. Averageresonanceneutron capture (ARC) has been shown to yaeld complete sets of (usually) low-spin states below a certain energy. It is shown how the concept of completeness can be extended to charged-particlefusion reactions, which can probe nuclei at higher spins and further awayfrom the line of stabihty.

A large body of experimental data is required for testing nuclear structure models. The presence or absence of a particular level can be crucial. A historical example is the difference between quadrupole vibration [ 1 ] and ?-unstable [2 ] patterns with regard to the energy of the O + level. Moreover, the identification of experimental with theoretically predicted levels requires detailed information whenever the number of levels of a particular spin and parity is large in a given energy interval. Neutron-capture spectroscopy has proven to be an excellent instrument for nuclear structure studies. It presents some very attractive features, in particular the possibility to obtain directly the level energies by subtracting the primary capture T-ray transition energies from the neutron binding energy, and also to observe secondary T-ray transitions and conversion electrons using high resolution crystal and magnetic spectrometers, respectively (see e.g. refs. [3,4] ). But the advantage to be stressed here is that with the average resonance capture (ARC) method complete sets of levels in certain spin arrd excitation-energy ranges can be populated. This was recognized very early [ 5,6 ]. In addition, the knowledge about the completeness of the sets can have very interesting consequences, as discussed by Casten et al. [7 ]. Neutron capture, however, has one major limitation, that of populating in general a rather narrow range of spins. Moreover, only a limited number of nuclei, close to the stability limit, can be excited.

It is therefore natural to examine if other non-selecttve reactions, populating a broader range of spins and nuclei, can also present completeness properties. Inelastic neutron scattering (INS) has been advocated by Yates and the Kentucky group [ 8 ]. However, the method has not enjoyed widespread application. Von Brentano et al. [9 ] have claimed that fusion reactions at the barrier have completeness properties. The subject of this letter is to generalize this property to (light-ion, xn) reactions and to show that a region in the level-excitation energy versus spin plane can be delimited where the level scheme obtained can be reliably regarded as complete. What is proposed here is a new precise method for the determination of this region of completeness. This relies on experimental regularities in the side-feeding population which are well supported by statistical calculations (see below). A consequence of such knowledge of completeness will then be presented for illustration. Finally the merits and limitations of completeness determinations in neutron-capture and in fusion reactions will be compared. It is well known that the slopes of the excitation functions in (particle, xnT) reactions are spin dependent and can therefore be used to assign spins. The side-feeding intensities (computed from the intensity balance between observed transitions populating a level and discrete transitions depopulating it) are also dependent on the level spins and excitation ener-

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gies. This is illustrated fro the lOSpd(~t, 2nT) 1lOCd reaction [ I 0 ] in fig. 1. It was shown by Kern et at. that by combining the information derived from the excitation slopes and side-feeding intensities (ESSI method [ 10 ] ) to the results of angular distribution measurements, the spins and parities of a very high fraction of the observed levels can be assigned. Table 1 illustrates this for recent studies of 110Cdand 112Cd" It is apparent from fig. 1 that the side-feeding intensities display a noticeable regularity. This property is not fortuitous and it was possible to reproduce these data by a statistical calculation [ 12,13 ] using the computer program CASCADE [ 14] and a newly developed program. The important point to be tested is the degree to which the side-feeding population is non-selective. The ratios of the experimental sidefeeding intensity (A,f) exp to the computed intensity (A,f) ~ for the spin 6 levels in l~°Cd are presented in

7

~" 60t

~,~

4~.

6.

\

lo 9 ' X 12

'l°cd

..............

fig. 2. Spin 6 was selected because the largest number of levels was observed for that value. The experimental data are for the reaction l°Spd((t, 2nT) at E~=27.1 MeV [10] and the calculation is described in ref. [ 12 ]. An arbitrary normalization factor was used since the experimental results are only relative. It is apparent that there is a very good agreement within ~ 10%, while the cross section varies by a factor of 5 between the lowest and the highest energy level. The intensity to the positive and negative parity levels is equally well reproduced. There are no systematic differences between the population of the ground-state (g.s./spherical), intruder ( I / d e f o r m e d ) , o r quasigamma (q-T/asymmetric) band I = 6 + levels. In addition, no previously known I = 6 level, established in many different experiments performed on 1lOCd' was missed. Whereas the Cologne group has shown (see e.g. ref. [ 9 ] ) that the side-feeding population of selected levels as a function of the projectile energy can be reproduced by statistical calculations, we show here that the side-feeding population of all levels as a function of their excitation energy is regular and nonselective. This can easily be understood since the sidefeeding population originates from the continuum

"~ 11

12~2]i]

.v , 1

~

1001

, 21 ],{I 0

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P (1809 keV) o Negatwe panty . • UnPmovcnpanty , , , , 2 3 4 5 MeV Level excitation energy

~ gs

20

q-i I

2'.5

3'o

3'5

Eexc [MeV]

Fig. 1. Side-feeding intensities for the 1°Spd(t~, 2n T) i 1OCd reaction [ 10] reported as a function of the level excitation energtes. The bombarding energy was E~= 27.1 MeV The solid lines connect the data points corresponding to the same spin values There is no difference according to parity, except for spin 8 which is unexplained (no such parity dependence occurs m 112Cd). The dotted horizontal lane indicates the lower limit of completeness. The star is discussed in the text.

Fig. 2. Ratios of the experimental [10] to the calculated [12] side-feeding intenslues of the 1=6 levels for the l°SPd(u, 2nT) l~°Cd reaction. The dots are for posture parity, the open circles for negative-parity final states; g.s. stands for "ground state", I for "intruder" and q-T for "quasi-gamma" (see text). The error bars represent the statmtical error ( 1 a) only. To apprecmte the deviations and the spin sensitivity, note that the ratios A~f(1)/A,f(Io=6) are about 0.5 and 2.2 for 1=5 and 7, respectively, at Eoxc= 3 MeV These numbers are far off-scale.

Table 1 Number of levels observed and assigned m 11°'1~12Cd.

8

Nucleus

Reference

ReacUon

Number of observed levels

Number of spin assignments

Number of spin and parity assignments

11°Cd 112Cd

[10] [ 11 ]

(u, 2nT) (u, 2uT)

60 83

56 79

54 67

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states. The number of possible feeding paths is very large so that an averaging is taking place and particular configurations do not play any appreciable rote. This guarantees an average side-feeding population of all levels. The similarity with ARC is obvious. In order to determine the hmit of completeness, the lowest intensity limit of the transitions assigned [ 10 ] by coincidence must be assessed. In al°Cd this is approximately 3 units for transitions below 500 keV, and 2.5 units above 500 keV, using a relative scale where the 2 + -~0 + transition has the intensity 1000 units. Only three observed transitions with intensities around I t = 6 could not be placed in the scheme. Therefore, it can be stated with confidence that no levels with a side-feeding intensity larger than 7 units

MeV 5-

laoCd

4-

~" y r a s t line ©

zone of c o m p l e t e n e s s

V[ //

0

2

• Observedm (a,2nT),spin defimte 0 Not observed m (ct,2n-/),spin defunte or probable

4

6

8

10 SPIN

12

14

h

Fig. 3. M a p o f c o m p l e t e n e s s i n t h e level e x c i t a t i o n e n e r g y v e r s u s

spin planefor the l°8Pd(a, 2n~t)U°Cdreaction.In the figureother wellestabhshedlevels (observedin at least two differentexperiments) are also reported. (see fig. 1 ) have been missed. The figure chosen makes provision for a possible depopulation by more than one transition, considering that the decay of a level by more than two transitions of about equal intensities is empirically very unlikely. The corresponding spin versus energy diagram is displayed in fig. 3. The upper limit of completeness, Em~, for a

6 January 1994

given spin is derived from the interpolated or extrapolated intersection of the side-feeding intensity versus level energy functions with the intensity limit set at 7 units (see fig. 1 ). It is obvious that Em~xdepends on the sensitivity achieved in the experiments and is not a general limit of the method. In the marked region, the population of any level is guaranteed to be large enough for its observation. By this method, and for the first time in fusion reactions, the concept of completeness is made quantitative and operative. The important consequences of completeness in nuclear structure studies have been stressed in several publications and they will not be dwelled on here. Instead, an illustrative problem regarding a specific level at 1809 keV in n°Cd will be presented. It will exemplify the kind of conclusions which can be drawn: in their study of the xl°mIn(2+) decay, Sarantites et al. [15] observed a 1151.5(8) keV transition and suggested that it depopulates a 1809.0 keV level. A transition with the same energy was observed in the l°8Pd(a, 2n)U°Cd reaction [10] and tentatively identified with the former, indicating an upper value o f / = 2 for the initial level. More recently Wesseling et al. [ 16 ] observed a 1809 keV level in an (e,e') experiment on U°Cd. They concluded that its spin and parity is 4 +, although spins 2 and 3 could not be excluded. From an inspection of fig. 1, it is apparent that a spin 4 (see the star in the figure) or a spin 3 level would have a side-feeding population of about 37, respectively 20 units, which represents a minimum value, since the level can also be fed by discrete transitions. It could not possibly have escaped observation. A spin 2 level would lie close, but still within the completeness limit (fig. 3) and would have a minimum (side-feeding) population of ~ 8 units, much larger than the observed intensity (1.3 units) of the 1152 keV transition [ 10 ]. We thus conclude to the inexistence ofa 1809 keV level on the basis of the completeness region defined in fig. 3. In confirmation of this conclusion, it is noted that the 1152 keV transition observed in ~°8Pd(a, 2n) reaction studies was assigned to u ~Cd by Kumpulainen et al. [ 17 ] and that the transition with the same energy observed in the decay of 11°rain was shown by Bertschy [ 18 ] to depopulate a level at 3314 keV. The 1809 keV level was observed neither by Araddad et al. [ 19 ] nor by Pignanelli et al. [20] in their scattering studies of H°Cd, confirming the non-existence of the level. The

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above example shows that the knowledge about the m i n i m u m (side-feeding) population o f a level is particularly useful to discuss the existence o f a level with a given spin observed in another experiment or expected on theoretical grounds to lie in some energy interval. Finally, it is proper to c o m m e n t on the reliability o f the present method and to compare it with ARC. One problem could be the presence o f isomers. In an even nucleus, the isomer decay path goes necessarily through the 2 + level and will be apparent by a longtime component in the 2 + ~0~- transition. N o isomers were detected in l l ° C d and l~2Cd. When applying the method to an odd or o d d - o d d nucleus, it might be necessary in some cases to cut away a piece at the bottom of the region o f completeness in fig. 3, so that for a given spin the energy range will not be from 0 to Em~x but form Em~n ¢ 0 to Em~x, the lower limit depending on the energy threshold for the detection o f the transitions. Another pitfall can be a level decaying solely by a ground state transition. This, o f course, applies only to initial levels close in spite to that o f the ground state. That is, in an even nucleus, levels with spin 2 or lower. It is therefore necessary to observe singles transitions up to an energy higher than the corresponding "completeness" limit of the relevant spin window, e.g. ~ 1860 keV for spin 2 in ll°Cd (see fig. 3). In the same way, a level with spin 4 could decay by a single transition to the 2 + level. To ensure its observation and, therefore, completeness in the spin 4 window, the measured energy range should extend up to the corresponding limit ( ~ 2800 keV, see fig. 3) minus E ( 2 +) = 6 5 8 keV, i.e. ~ 2 1 4 0 keV. Similar ranges have to be estimated for the higher spins. This was not yet realized when the experiments on H°Cd were performed. In theory, however, the A R C method does not suffer from such limitations. In practice, the mherent, relatively low resolution o f semiconductor detectors for (primary) transitions o f several MeV is a problem and, therefore, the decay of the directly populated levels must also be established. This can be very difficult in some cases (see, e.g., the problem o f 192Ir, ref. [21 ] ). The use o f high resolution crystal spectrometers will allow one, in general, to observe the decay of the observed levels in a broad range o f energies. Crystal spectrometry in fusion reactions does not have a comparable power at this time and is not 10

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o f widespread use [22 ]. It has also to be noted that the application of the concept o f completeness derived here from the side-feeding intensity properties has not yet been applied to strongly deformed nuclei. It is known that for these nuclei the slope o f the excitation functions depends not only of the spin but also on the quantum number K (see, e.g., ref. [23 ] ). A theoretica~ and experimental investigation o f the side-feeding properties in deformed nuclei is ongoing. In conclusion, this paper shows that the concept of completeness can be extended beyond fusion reactions at the barrier, that the reaction is non-selective, that the side-feeding intensities vary regularly as a function of level spins and excitation energies, so that an estimable m i n i m u m population of the levels in a well defined region of the spin versus energy plane can be guaranteed. A region of completeness can thus be determined. The author is grateful to R.H. Siemssen and R.F. Casten for useful discussions. This work was supported in part by the Swiss National Science Foundation and by the Paul Scherrer Institute (PSI).

References [ 1 ] G. Scharff-Goldhaberand J. Weneser, Phys. Rev. 98 ( 1955)

212. [2]L. WiletsandM Jean, Phys. Rev. 102 (1959) 654. [ 3 ] H.R. Koch et al., Nucl. Instrum Methods 175 (1980) 401. [4] W. Mampe et al. Nucl. Instrum. Methods 154 (1978) 127. [ 5 ] L M. Bolhngerand G.E. Thomas, Phys. Rev. Lett. 21 (.1968) 233. [6] R.E. Chrien, Trns. N.Y. Acad. Sci 44 (1980) 40 [7] R.F. Casten, D.D. Warner, M.L. Stelts and W.F Davison, Phys. Rev. Lett. 45 (1980) 1077. [8 ] S.W. Yates, in: Capture gamma-ray spectroscopy, ed. R W. Hoff, Alp Conf. Proc. No. 238 (ALP,New York, 1991) p. 218. [9 ] P. yon Brentano et al., Nuclear structure of the Zr region, eds. J. Eberth, R.A. Meyer and K. Sistermch (Springer, Berhn, 1988) p. 157. [ 10 ] J. Kern, A. Bruder, S. Dnssl, V.A.Ionescu and D Kusnezov, Nucl. Phys. A~512 (1990) 1. [ 11 ] M. D616ze,S. Drlssi, J. Jolie, J. Kern and J.P. Vorlet, Nucl. Pbys. A554 (1993) 1 [ 12] J. Kern, P. Cejnar and W. Zipper, Nucl. Phys. A 554 (1993) 246. [ 13 ] P. Cejnar and J. Kern, Nucl. Phys. A 561 ( 1993) 317. [ 14] F. Piihlhofer, Nucl. Phys. A 280 (1977) 267.

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[ 15 ] D.G. Sarantites, N.R. Johnson and H.W. Boyd, Nucl. Phys. A 138 (1969) 115. [ 16] J. Wesseling, C.W. de Jager, J.B. Van der Laan, H. de Vrles and M.N. Harakeh, Nucl. Phys. A 535 ( 1991 ) 285. [ 17 ] J. Kumpulalnen et al., Phys. Rev. C 45 (1992) 640. [18]M. Bertschy et al., Proc. 8th Intern. Symp. on Capture gamma-ray spectroscopy (Fnbourg, 1993), ed. J. Kern (World Scientific, Singapore) in press; and to be pubhshed. [19] S.Yu. Araddad et al., Yad. Fiz. 52 (1990) 3 [Soy. J. Nucl. Phys. 52 (1990) 1].

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[ 20 ] M. Pignanelll et al, Nucl. Phys. A 540 ( 1992 ) 27. [21 ] J. Kern et al., Nucl. Phys. A 534 ( 1991 ) 77. [ 22 ] B. Perny et al., Nucl. Instrum. Methods A 267 (1988) 120, A. Bruder et al.,Nucl. Phys. A 467 (1987) 1, S. Drlssl et al., Nucl Phys. A 543 (1992) 495. [23]S. Olbnch, V. Ionescu, J. Kern, C. Nordmann and W. Reichart, Nucl. Phys. A 342 (1980) 133.

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