Investigation of giant E3 resonances by (N, γ) reactions

Investigation of giant E3 resonances by (N, γ) reactions

2 .B : 3.A Nuclear Physics A321 (1979) 354-364 ; © North-Holland PabILrhlnp Co., Antaterdatn Not to be reproduced by photoprint or microfilm without...

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2 .B : 3.A

Nuclear Physics A321 (1979) 354-364 ; © North-Holland PabILrhlnp Co., Antaterdatn

Not to be reproduced by photoprint or microfilm without written permLsion from the publisher

IIWFSTIGATION OF GIANT E3 RESONANCES BY (N, y) REACTIONS F. SAPORETTI and F. FABBRI

Comitato Nazionale Faergia Nucleare, Centro di Calcolo, Bologna, Italy

and R. GUIDOTTI Facoltà di Ingegneria dell'Università, Bologna, Italy

Received 29 December 1978 Abstract : E1Fecta related to the presence of giant E3 resonances are investigated by nucleoa radiative capture according to the direct-semidirect model. The y-ray angular distributions from the zoepb(IV ; yo) reactions are calculated is the energy region above the giant dipole resonance and the influence of the El-E3 and E2-E3 interferences is discussed. The results provide indications of an appreciable effect on the 90° photon emission when a collective isovector E3 excitation is present.

I . IDh'OdUCtiO~ Giant resonances with multipolarities other than electric dipole have been a subject of increasing interest in the last few years. Data have been accumulated so far from electron and hadron scattering, from photonuclear reactions and radiative capture experiments. In several cases the direct-semidirect model for nucleon radiative capture t-4) seems to provide an appropriate framework for discussing effects related to the multipole capture processes; in particular, model calculations of photon angular distributions offer a valuable tool for investigating the presence of multipole radiations interfering with the dominant dipole one. These facts have served to stimulate efforts towards theoretical developments and refinements of the interaction model. Up to now, however, theproposed model has dealt with electricdipole and quadrupole capture (see, e.g., ref. S)) ; magnetic dipole capturehas been recently considered too 6). The aim of the present paper is to extend the model to include capture proceeding via giant electric octupole resonance states, in addition to the collective El and E2 excitation modes of the target ; the direct process is also included . This extension allows us to investigate the presence of giant E3 resonances by E1-E3 and E2-E3 interference effects. Here we present the results for the (n, y°) and (p, y°) reactions on Z°BPb ; in this nucleus different electroexcitation experiments ' - 9) have shown evidence for an isoscalar octupole resonance at nearly 16-19 MeV; on the other hand the isovector 354

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35 5

octupole strength is expected to exhaust a large fraction of the energy-weighted sum rule around 33 MeV [ref. 1 °)]. First, a comparison between the strengths of the different mechanisms participating in the octupole capture is presented. Then the photon angular distributions from neutron and proton capture are investigated in the 12-35 MeV and 200 MeV energy intervals, respectively, where E3 radiation should be more clearly revealed. Particular attention is focused on analysis of the asymmetries characterizing y-ray angular distributions. Results point out an increase of the 90° radiation in the presence of an isovector octupole resonance. 2. Mathematical formulation

Following the formalism originally proposed in ref. s) and then applied in refs . s .6), we derive the complex particle-vibration coupling Hamiltonian for isoscalar (T = 0) and isovector (T = 1) collective octupole modes, HE3

=

~

~Pl'~3P ,

~ il(7~(r)T3 Y3Y(e'

T=O, 1 p

where the one-body operators A

a3p - ~ T3iri Y3~(Bi+ i= 1

~Pi)

represent the collective octupole coordinates of the target. The symbols i a , r, 8, ~P denote the isospin and the spherical coordinates of the incident particle, while i3t, ri, Bi, ~P; refer to the target nucleons. The radial volume form factor is obtained as

where the P(T°~ are the strengths of the two-body forces and the total nucleon density Considering the coupling interaction H' ~= HÉ 1 +Hé 2 +HÉ3 as a perturbation, we calculate the electric transition matrix elements to first order as a sum of direct and semidirect terms, viz. Qz,~f = C~`rl~°z~l`~ii + T=O. 1

Ey-~z~+~il'x~

EY

+~x +~iT~

In previous treatments, the third term, corresponding to the perturbation eßect on the final state, has been neglected ; we now retain the latter for its significant contribution in the energy region considered here . In the last equation, .il°x~, is the usual electric multipole operator of the system ; the energy EY refers to the emitted photon

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F. SAPOREITI et aJ .

and the parameters itWx and ~~ express the excitation energy and the decay width of the (.i, T) collective state; in the electric dipole case (~, = 1) we have only the isovector team (T = 1). The incident, intermediate and final state wave functions are respectively given by ~i = ~ e~°~ "[4~(2f + 1)].~(f ZOm'11"m'~1" ~"~fr,"1" (rkPoo~ 1 "J. ~`r = ~~ui>(rkPoo~

Here fj'm' and ijm are the quantum numbers of the initial and final states of the incident particle, tr,. is the Coulomb phase shift (Q, " = 0 for incoming neutrons gyp are the spin angular wave functions and ~Pxw is the wave function of the target nucleus in the giant (.~, T) state. The integrated cross section for E3 radiative capture of a nucleon into a single particle bound state (l,j) is then given by _ 16~c MkY ,~ f 2 rr,~(E3) _ 33075 ~tZk' ~~IQs I ,

where M is thereduced mass, and k' and k~ are the incident and photon wave numbers. The differential cross section for unpolarized nucleon radiative capture is expressed by 4 M C~+ 1 ~~ ~~r * Iz ~= I I z ~+~ ~_ where X~, _ [~~+1)]-~LY,~, are the vector spherical harmonics. Expanding in Legendre polynomials by means of some Racah algebra, we derive 6 =i

with v the integrated cross section and E the incident nucleon energy . The coefficients a ofthe expansion are related to the multipolarities involved in the emission process ; the odd coefficients reflect the interference between radiations of opposite parity, while the even ones reflect the interference between radiations of the same parity . 3. Cakalatione The object of investigation is here the radiative capture of neutrons and protons by ~°BPb in the energy region above the giant dipole resonance. The initial wave functions are calculated according to the optical potential 11). The real part of the same potential is used to calculate the bound state wave functions. The depth of

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the potential is adjusted to give the experimentally known binding energies of the single-particle states, that is 3.94 MeV for the 2gß neutron state and 3.8 MeV for the lh.t proton state . A complex volume form' z) in the particle-vibration coupling with real and imaginary strengths equal to -50 MeV (T = 0) and 130 MeV (T = 1) is used. Giant multipole resonance parameters used in calculations are summarized in table 1. In order to estimate the transition matrix elements between the ground and the giant multipole states, a direct use of the measured strengths B(E~,) is made. The data are taken from photonuclear reactions ts, ia) and inelastic electron scattering e). The strength of the giant isovector octupole resonance, not identified so far to our knowledge, is deduced from the results of ref. '°) ; the transition strength calculated in the random phase approximation is expected to exhaust 58 ~ of the energyweighted sum ruleevaluated from thedouble commutator in the energy region around 33 MeV. 1 Giant multipole resonance parameters for =°8Pb used in calculations Te RI F

E~.

dT

iuox (MeV)

B(Ex)

!' (MeV)

Ref.

El E2 E2 E3 E3

1 0 1 0 1

13 .42 10.5 22.5 17.5 33

65 ~2 6.7 x 10 2 fm a 4.2 x 102 fm 4 3.2 x 10' fmb 58 % EWSR

4.05 2.8 5.0 4.2 5

in . ~4 ) e) e) e) io)

4.1 . THE Zoepb(n, Yo) REACTION

4. Results And dlscossioo .

The integrated cross section for octupole neutron capture to the 2g.t ground state ofs° 9 Pb in the 12-35 MeV energy region is shown in fig. l. Thedominant contribution to the cross section clearly arises from the giant isovector resonance ; this exhibits a peak at 30 MeV about twenty times higher than the isoscalar peak at 14.5 MeV. This is mainly due to the strong energy dependence of the cross section through the factor k~/k', which greatly favours the resonance located at the highest energies, though the transition matrix element values are similar at the peaks of both resonances . The octupole direct mechanism does not give any appreciable contribution to the cross section, this capture being strongly inhibited by the neutron eBective charge. In fig. 1 the integrated cross section for the quadrupole capture process, characterized by a resonancelike shape mainly of isovector nature, is âlso presented. In the interval considered the dipole capture, with its peak around 10 MeV, is rapidly decreasing ; however, the E2 and E3 capture are low compared with the El dominant process, and this suggests that only interference processes between E3 and El, E2 radiations could reveal eßects arising from the presence of a giant isovector octupole

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F. SAPORETTI et al.

a _s

b

18

-*--r

24

En ( A1~1/ ~

Fig . 1 . Integrated cross sections for octupole and quadrupole neutron capture to the 2 g9r~ ground state of = °9Pb .

resonance. Thus the y-ray angular distributions are a suitable means for undertaking this investigation. The energy dependence of the Legendre coefficients a, characterizing the angular distributions of the radiation emitted in the capture process, is illustrated in fig. 2. The dashed curves are obtained by taking into account only the dipole and quadrupole processes ; the continuous lines are calculated by adding the isoscalar and

Fig. 2 . Coefficients a, versus the incident neutron energy for the'°sPb(n, yo) reaction. E1+E2 (dashed line), E1+E2+E3 (continuous line) .

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isovector octupole contributions. As expected, comparison between the two curves shows low effects from the isoscalar E3 process ; below 20 MeV the latter increases the a 1 negative peak by El-E3 interference and produces positive a 4 values . Larger effects arise from the presence of an isovector octupole capture at higher energies ; around 30 MeV, clear peaks appear in the curves of odd and even coefficients - in a t generated by the E2-E3 interference and in a 1 , a 4 by the El-E3 process. Calculations show no modification to the a 3 coefficient and positive values for the coefficients a s and a 6 arising from the E2-E3 interference and pure E3 radiation, respectively . Starting from this picture of the properties of y-ray angular distributions, we fmd it useful to assume the following quantities : W(6) -

1--'Za1 +ea4 -bab -1 2Y(1Lrc) -1, 1+a1P1(cos 9)+aaP4(cos B)+a6P6(cos B) Y(9)+Y(~t-B)

a Y(B)- Y(n-B) t Pt(cos 9)+a 3P3(cos 6)+as Ps (cos B) 1(6) Y(B)+ Y(a-B) 1 +a 1P1(cos B)+a4P4(cos 9)+a6 P6 (cos 6) The first ratio, in a sense, weighs the 90° photon yield with respect to the average yield at two 90° symmetric angles ; the second ratio measures the fore-aft asymmetry of the photon angular distributions The connection of these factors with the interference processes remains well established by the combinations of odd and even coefficients appearing in the expressions given. In fact, the interference ofany octupole radiation, present along with the quadrupole radiation, affects the odd coefficients a t , a 3, as, while interference with the dominant dipole radiation interests only the even coefficients a1 and a 4 ; the pure E3 contribution is negligible, though it is for example the sole cause of the positive a 6 values . In fig. 3 the calculated W(50°) and 1(50°) factors are plotted versus the incident neutron energy for the El +E2 processes

Fig. 3. Energy dependence of the factors W(50°) and I(50°) for the =°°l?b(n, y°) reaction . El +E2 (dashed line), E1+E2+E3 (continuous line).

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F. SAPORETTI et a!.

(dashed line) and E1+E2+E3 processes (continuous lines). The comparison of fig. 3a shows clear effects generated by the octupole giant resonances and related to the El-E3 interference ; for instance, in all the energy range considered the 90° photon emission is favoured by the octupole mechanisms . However, what strikes us most are the two pronounced peaks of the W-factor, when octupole capture is present: at 16 MeV and 30 MeV there appears an increase of ~ 16 % (T = 0) and ~ 130 (T = 1~ respectively . This suggests that experimental confirmation of this effect, which is particularly marked for the isovector case, would be a sign of the presence of collective E3 excitations. On the other hand, fig. 3b shows that the E2-E3 interference process by the odd coefficients scarcely alters the fore-aft asymmetry of y-ray angular distributions; only around 30 MeV does the forward emission present a small attenuation. With the foregoing considerations in mind, we can interpret the results shown in fig. 4. This displays the y-ray angular distributions calculated for 30 MeV neutron capture. To make the results stand out, the angular distributions are folded about 90° ; the labels "f" (forward) and "bH (backward) . indicate the curves related to the angular intervals 0°~9(P and 90°-180°, respectively. The dashed and continuous lines represent the same capture cases as in figs. 2 and 3. In both curves we can observe a forward-peaking photon emission arising from the dominant El-E2 interference by the a l and a3 weffcients . A displacement of the differential cross section peak towards 90° appears when the octupole process is included in the calculations (con~tinuous line). The shift follows mostly from the El-E3 interference, and thus from the aZ and a4 coefficients ; a coherent effect from the al coefficient is also present. 4.2 . THE ~ oe pb(P, Yo) REACTION

The results of cross section calculations carried out for octupole proton capture to the lh~. ground state of z °9Bi in the 20-40 MeV energy range are displayed in fig. 5. This shows the integrated cross section (continuous curve) and, separately, the contributions of the two mechanisms responsible for the E3 radiation, i.e. direct capture (dot-dashed curve) and collective isovector capture (double-dot-dashed curve) . The isoscalar mechanism is absent, owing to the Coulomb barrier effect which greatly reduces the transition matrix elements at low energies. The same effect is also the reason for an appreciable E3 emission from the direct process being confined to energies above 30 MeV. As can be seen in the figure, an interference mechanism between direct and collective isovectar capture is present, destructive below 29 MeV and constructive above. It appears, however, that for proton capture, as for neutron capture, the octupole strength is relatively small compared with the strong dipole one. Thus the same conclusions hold : any E3 erect which may be present has to be searched for by the properties of the y-ray angular distributions. The coeffdents a describing the y-ray angular distributions are plotted versus the incident proton energy in fig. 6. The dashed curves correspond to dipole and quad-

GIANT E3 RESONANCES

36 1

A Fig. 4. Angular distribution of y-rays emitted in the '°s Pb(n, Yo) reaction. El +E2 (dashed line), E1+E2+E3 (continuous line). Labels "f' and "b"indicate the curves of the angular intervals 0°-90° and 90°-180°, respectively .

Fig. ~. Comparison between the wntributions of the different capture mechanisms to the intograted octupole cross section (continuous line) for the'°sPb(p, y°) reaction . Direct capture (dot dashed line), collective isovxtor capture(doublodot-dashed line).

Fig. 6. Coefficients a, versus the incident proton energy for the ~°ePb(p, y°) reaction . El +E2 (dashed line), E1+E2+E3pa (dotted line), E1+E2+E3 (continuous line).

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F. SAPORETTI e~ al.

rupole capture; on including the direct octupole capture we obtain the dotted curves ; the continuous curves represent the result of calculations when capture proceeding via the giant isovector octupole state is also added. The figure shows the influence of the octupole direct process on the a, and a 3 coefficients, partially attenuated by the collective isovector process at its resonance energy . More sizeable modifications, however, are exhibited by the even a 2 and a4 coeflicients ; indeed, in this case, the direct and isovector effects strengthen each other and evident bumps emerge . Calculations provide non-zero values for the a s coeffcient; the a6 coefficient (not plotted) is negligible. The energy dependence of the factors W(B) and I(B) calculated at 50° is shown in fig. 7. The same relations hold between curves and capture processes as in fig. 6. As can be seen in fig. 7a, the inclusion in the calculations of the direct E3 capture (dotted curve) gives rise to an appreciable increase of the 90° photon emission compared to the case ofEl + E2 capture alone (dashed curve) . The pronounced peak, characterizing the continuous curve, stems from the presence of a collective isovector octupole mechanism interfering with the dipole process. We note that at 30 MeV the dotted and continuous curves present increases of x 100 ~ and x 200 ~, respectively . This leads one to suppose that collective isovector E3 effects on angular distributions from capture on 2°a Pb could be recognized by high sensitivity experiments. Fig. 7b describes the fore-aft asymmetry of y-ray angular distributions ; a forward-peaking emission due to the dominant E1-E2 interference seems constantly present for energies above 24 MeV. The octupole capture, by its direct component, amplifies this behaviour, which is masked only by the influence of the collective isovector contribution in the neighbourhood of its resonance. The asymmetry factor I(50°) exhibits an increase of 40 % at 40 MeV.

Fig. 7. Energy dependence of the factors W(5(P) and I(SO°) for the =°ePb(p, y°) reactions . E1+E2 (dashed line), E1+E2+E3pQ (dôtted line), El+E2+E3 (continuous line).

GIANT E3 RESONANCES

36 3

â _s v bv

8 Fig. 8. Angular distributions of y-rays emitted from capture of 30 MeV and 40 MeV protons to the lly~ 2 ground state of Z°9 Bi . El+E2 (dashed line), E1+E2+E3 (continuous line) .

Thecalculated angular distributions ofy-rays following radiative capture of30 MeV and 40 MeV protons are presented in fig. 8. The connexion between curves and capture processes is the same as in figs . 6 and 7. As expected, at 30 MeV (fig. 8a) the fore-aft asymmetry of the angular distributions is weakly affected by the E3 process; in fact the coefficients at and a3 are practically indifferent to such a process and the coefficient a5 is not strong enough to produce evident effects. The displacement of the continuous curve towards 90° is due to the even coefficients aZ and a4, and therefore to the El-E3 interference. On the contrary, at 40 MeV (fig. 8b) an increase in the forward emission appears when a direct E3 radiation, interfering with E2 radiation, is present. 5. Conclosioos In order to extract information on the giant E3 resonances by nucleon radiative capture we have calculated the photon angular distributions in and above the giant dipole resonance region on the basis of the direct-semidirect model. In spite of the weakness of the E3 radiation we have learned that the 90° photon emission rises when an E3 mechanism is present ; for example, the 90° cross section, weighed over the 50°-130° average cross section, shows an appreciable increase at the peak energy of the giant isovector E3 resonance. This is in accord with the result that the main effect comes from the interference of the octupole radiation with the dominant dipole one, and is thus revealed in the even coelFtcients. On the other hand, the interference between octupole and quadrupole processes, affecting the odd coefficients,

36 4

F. SAPORETTI et al.

leads to a smaller effect. In short, the results would support the speculation that collective isovector octupole effects on (N, yo) angular distributions from a heavy nucleus such as 2°aPb should be rematkable, and thus recognizable by high sensitivity experiments. References 1) A. M. Lane, Nucl . Phys. 11 (1959) 625 ; A. M. Lane and J. E. Lynn, Nucl. Phys. 11 (1959) 646 2) G. E. Brown, Nucl. Phys. 57 (1964) 339 3) C. F. Clement, A. M. Lane and J. R. Rook, Nucl. Phys . 66 (1965) 273, 293 4) A. A. Lushnikov and D. F. Zaretsky, Nucl . Phys . 66 (1965) 35 5) F. Saporetti, G. Longo and R. Guidotti, Phys. Lett . 76B (1978) 15 6) F. Saporetti and R. Guidotti, Lett. Nuovo Cim. 22 (1978) 202; Nucl . Phys . A311(1978) 284 7) M. Nagao and Y. Torizuka, Phys . Rev. Lett . 30 (1973) 1068 8) R. Pitthan, F. R. Buskirk, E. B. Dally, J. N. Dyer and X. K. Maruyama, Phys . Rev. Lett. 33 (1974) 849 9) M. Sasao and Y. Torizuka, Phys. Rev. C15 (1977) 217 10) K. F. Liu and G. E. Brown, Nucl . . Phys. A265 (1976) 385 11) L. Roses, J. G. Beery, A. S. Goldhaber and E. M. Auerbach, Ann. of Phys. 34 (1965) 96 l2) G. Longo and F. Saporetti, Nucl : Sci. Eng. 61 (1976) 40 ; Nucl . Phys . A199 (1973) 530 13) A. Veyssière, H. Bell, R. Bergère, P. Canoe and A. LeprEtre, Nucl . Phys . A199 (1970) 561 14) R. Bergère, H. Bell, P. Canoe and A. Veyssière, Nucl. Phys . A133 (1969) 417