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Electroexcitation of giant resonances in 58Ni
Volume 145B, number 1,2
PHYSICS LETTERS
13 September 1984
ELECTROEXCITATION OF GIANT RESONANCES IN 5 8Ni R. KLEIN, Y. KAWAZOE 1 Max.Planck-Institut ffir Kernphysik, D-6900 Heidelberg, Germany P. GRABMAYR, G.J. WAGNER Physikalisches lnstitut der Universitdt Tiibingen, D-7400 Tfibingen, Germany and J. FRIEDRICH and N. VOEGLER lnstitut ffir Kernphysik der Universitdt Mainz, D-6500 Mainz, Germany Received 6 June 1984
Response functions for inelastic electron scattering from 58Ni have been determined for momentum transfers ofq ~0.4-2 fm-1. A multipole decomposition of the full continuum for excitation energies below 35 MeV yields new features of the E1 and E3 strengths. The E2 strength is in excellent agreement with a-scattering data which demonstrates the usefulness of both probes and shows the isospin purity of the isoscalar giant quadrupole resonance.
Given the complexity of nuclear response functions in the giant resonance region, knowledge of giant resonances cannot be claimed unless compatibility of giant resonance excitation by different probes has been achieved. In 208pb ' strengths of the isoscalar giant quadrupole resonance (GQR) exhausting ~30%, ~80% and ~70% of the energy weighted sum rule (EWSR) have been deduced from low- [1] and highenergy [2] electron scattering and from hadron scattering experiments (ref. [3] and references therein), respectively. To some extent these discrepancies may result from background subtractions: while the background problems of hadron scattering experiments are notorious, the radiative tail of electron scattering spectra is calculable in principle, in practice, however, it is quite c o m m o n to subtract an empirical background as well (e.g. refs. [ 1,4] ). To study the compatibihty o f electron and hadron scattering experiments we chose the target nucleus 58Ni where also results obtained with various probes are available for comparison (ref. [4] and references 1 On leave of absence from Tohoku University, Sendai, Japan.
therein, refs. [ 5 - 7 ] ) . Furthermore radiative corrections are smaller than in 2°spb; we believe that they can be calculated with an accuracy permitting a meaningful interpretation of the corrected strength as nuclear response function. Ten (e, e') spectra covering excitation energies up to about 50 MeV were taken with a 50 mg/cm 2 isotopically enriched 58Ni target for elastic momentum transfers qel ~ 0 . 4 - 2 fm - 1 using beams of 124, 180 and 300 MeV electrons from the Mainz linear accelerator [8]. With the 180 ° spectrometer [8] an overall energy resolution of zXE/E < 10 - 3 was achieved. The resulting spectroscopic information on bound states has been published previously [9] * 1. In this letter we concentrate on the analysis o f the giant resonance region. Good counting statistics, a large range of momentum transfer and the absence o f instrumental background enabled us to perform a multipole analysis of the full continuum in 1 MeV wide bins. This procedure introduces much less bias than the B r e i t ,1 The 5.903 MeV group reported there turned out to be an unresolved multiplet of states. We take the opportunity to withdraw the 1(-) assignment and the B(E1) value. 25
Volume 145B, number 1,2
PHYSICS LETTERS i
Fig. 1. shows a spectrum taken at qel = 0.91 fm - 1 i.e. close to the maximum of the E3 form factor. Radiative corrections were calculated with an updated version o f the program described in ref. [2] using elastic form factors. The vanishing of count rates in between discrete states in the unfolded spectrum serves a a performance test and gives us confidence also for the giant resonance region, where the radiative corrections amount to less than 15% for q > 0.7 f m - 1. The response function W(q, ~) defined as d2o/dg2 dco divided b y the Mott cross section was decomposed into form factors FL(q) o f multipolarity L 6
i
58Ni(e.e') 150
E0=180MeV O =600
#, >=
~ 50
20
,tO
Ex
13 September 1984
[MeV]
W(q, co)= ~
Fig. 1. Spectrum of the SaNi(e, e') reaction for qel = 0.91 fm -1 with and without radiative unfolding (lower and upper curve, respectively). The (presumably isovector) giant octupole resonance near 13 MeV and the giant dipole plus quadrupole resonances around 16 MeV are clearly visible. The slight enhancement around 30 MeV is a reminiscence of a quasi-free scattering peak with strength contributions from several multipoles.
L=I
SL(CO) • IFL(q)l 2 ,
by a least-squares fitting procedure applied to determine the multipole strengths SL(CO). The q-dependence of the form factors was calculated with the DWBA program HADES [ 10] using Tassie transition densities based on the ground-state charge density from ref. [11]. (The same charge density was also used to calculate the radial moments required for the evaluation of the EWSRs leading to substantial dif-
Wigner peak fitting procedure following an empirical background subtraction which was applied e.g. in ref. [4].
58Ni(e, e') .q
I
00
Ex = 12 -13 MeV
i "
I
I
Ex =17- 18MeV
~
o
blC::
EII~
"01 "10 100 X
•
o
5
10
I
J
.5
1.0
.5
1.0 1.5 qeff/fm-1
2.0
.5
I
I
I
1.0
1.5
2.0
Fig. 2. Reduced cross sections for bound states of known spins and parities (left) and for energy bins where E3 strength (centre) and E2 strength (right) dominate. The latter are decomposed into DWBA form factors based on Tassie transition densities. Only full dots were included in the least-squares fit for L ~< 3 strength. Because of uncertainties in the shapes of the form factors we do not attribute the additional strengths at high q-values to multipolarities with L ~ 4. 26
Volume 145B, number 1,2
PHYSICS LETTERS
ferences with the sum rule values used in ref. [4]. These form factors yield excellent fits for low-lying collective states (see fig. 2 left). Their use in the giant resonance region, however, must be taken as one of several approximations of our method. (i) The factorization in eq. (1) is an essential assumption. A recent investigation of an RPA model response function shows that the ansatz is justified for small momentum transfers including the first maximum of the form factors [12]. (ii) Tassie form factors are exact for extremely collective states exhausting the full EWSR or if the doorway dominance scheme is valid [13]. In the opposite extreme of single-particle transitions, we have performed calculations in a continuum shell model without residual interactions in the spirit of ref. [14]. These calculations show that for excitation energies below 25 MeV the Tassie form factors represent a fair approximation also for high L-values which are the least collective in nature. (ii) Transverse excitations are neglected for the sake of simplicity. The maximum scattering angle was 85 ° and, in fact, in the bound-state region [9] no signature for transverse excitation was observed. Furthermore, the continuum shell model calculations [14] indicate that less than 15% of the total cross section is of transverse nature even at the maximum scattering angle. Therefore we believe that the approximations warrant reliable results in the low-L (L ~< 3), low-co (co < 30 MeV) and low-q (q < 1.3 fm - 1 ) region. For the energy bins at 12.5 and 17.5 MeV the decompositions are shown in fig. 2 (centre and right). B(EL) values per MeV resulting from the fitting procedure are presented for L = 1,2 and 3 in fig. 3. The error bars denote uncorrelated statistical errors. The E1 strength distribution exhibits a clear picture of the giant dipole resonance (GDR). Comparison with photonuclear results [15] shows good agreement in absolute magnitude and shape in the peak and the high-energy slope. However, we observe in addition a low-energy component at about 12 MeV which evades observation in photonuclear processes due to threshold effects. This component is also visible but less pronounced in ref. [4] and also in earlier electron scattering work [16] but was interpreted [17] as GQR. We feel that in the light of the present result the discussion on the isospin splitting o f the GDR (see e.g. ref. [18]) should be resumed.
13 September 1984 i
I
'
I
'
I
'
58Ni(e, e')
2.0
E1
~----,1.5
E
~ 1.0 IJ.l
0.5 --~l. 3
200
[
~1501
12~
•100H[
10w
,,,5011~ c~.~'~,~/
8~o -o "o
6b
10]-~1" 'tn
~
E3
-
2
1.1.1
No
0
10
20 30 40 Ex [MeV] Fig. 3. Strength distributions (histograms) with uncor[elated statistical error bars. The E1 strength is compared to results from photonuclear reactions [15]. The comparison of the E2 strength with an (c~,a') spectrum [6] (right hand scale, suppressed zero point) shows agreement in shape and magnitude (see text) for the isoscalar GQR riding on a smooth "background" (dashed line) assumed in the (a, c/) analysis.
The E2 strength shows a GQR at about 16 MeV on top of a smooth continuous E2 distribution. The latter may contain some E0 strength which is indistinguishable with the present method and which is known to lack concentration [19]. The GQR structure on top of the dashed line exhausts 26% of the electromagnetic EWSR. For comparison we also show in fig. 3 an (a, ~') spectrum [6] taken at 01a b = 11 °, i.e. in a maximum of the L = 2 angular distribution. The comparison is absolute: the (55 -+ 15)% of the isoscalar E2 EWSR known from (a, a') experiments 27
Volume 145B, number 1,2
PHYSICS LETTERS
[20] to reside in the resonance structure (above the dashed line) was converted into B(E2) values. The excellent agreement of the GQR properties determined with isoscalar and electromagnetic probes makes us confident that the problems occurring in the analysis have been dealt with appropriately. And then, as a result, the agreement shows a high degree of isospin purity of the GQR which contrasts to the isospin impurity of the GQR in 118Sn reported recently [21]. Since only ~55% of the isoscalar EWSR is exhausted by the GQR proper, part of the continuous E2 strength underneath the GQR is likely to be of isoscalar nature too. Such smoothly distributed strength cannot be unraveled from the background in hadron scattering experiments. Our data do not confirm the existence of an isovector GQR at about 32 MeV reported by ref. [4]. The E3 strength distribution exhibits a fragmented isoscalar low-energy octupole resonance below 10 MeV which exhausts 16% of the isoscalar EWSR and a second E3 resonance near 13 MeV which is presumably of isovector nature because it was not observed in any a-scattering experiment. It exhausts ~28% of the isovector EWSR. As the analysis at the high momentum transfers is particularly dependent on the assumptions about the shape of the form factors, we conclude only very tentatively that the missing E3 strength resides above 35 MeV excitation energy. In summary, in addition to new information on giant dipole and octupole resonances in 58Ni the present work exhibits excellent agreement of GQR properties studied by electrons and a-particles, re-
28
13 September 1984
spectively. In view of the difficulties mentioned above this agreement is far from being trivial.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10[ [11] [12]
[13] [ 14] [15] [16] [17] [ 18] [19] [20] [21]
G. Kfihner et al., Phys. Lett. 104B (1981) 189. M. Sasao and Y. Torizuka, Phys. Rev. C15 (1977) 217. H.P. Morsch et al., Phys. Rev. C28 (1983) 1947. R. Pitthan et al., Phys. Rev. C21 (1980) 147. M.T. Collins, C.C. Chang, S.L. Tabor, G.J. Wagner and J.R. Wu, Phys. Rev. Lett. 42 (1979) 1440. K.T. Kn6pfle et al., J. Phys. (NY) G7 (1981) L99. B. Donin et al., Contributed paper HESANS 83 (Orsay) p. 31. H. Ehrenberg et al., Nucl. Instrum. Methods 105 (1972) 253. R. Klein et al., Nuovo Cimento 76A (1983) 369. H.G. Andresen, private communication. C.W. de Jager, H. de Vries and C. de Vries, At. Data Nucl. Data Tables 14 (1974) 491. J. Decharg~, D. Gogny, B. Grammaticos and L. Sips, Phys. Rev. Lett. 49 (1982) 982; D. Gogny, private communication. T.J. Deal and S. Fallieros, Phys. Rev. C7 (1973) 1709; G.F. Bertsch, Phys. Rev. C10 (1974) 933. Y. Kawazoe, G. Takada and H. Matsuzaki, Prog. Theor. Phys. 54 (1975) 1394. S.C. Fultz, R.A. Alvarez, B.L. Berman and P. Meyer, Phys. Rev. C10 (1971) 608. I.S. Gul'karov et al., Sov. J. Nucl. Phys. 9 (1969) 274. V.M. Khvastunov et al., S ov. J. Nucl. Phys. 25 (1977) 491. E.M. Diener, J.F. Amann, P. Paul and S.L. Blatt, Phys. Rev. C3 (1971) 2303. U. Garg et al., Phys. Rev. C25 (1982) 3204. D.H. Youngblood et al., Phys. Rev. C23 (1981) 1997. J.L. Ullmann et al., Phys. Rev. Lett. 51 (1983) 1038.
PHYSICS LETTERS
13 September 1984
ELECTROEXCITATION OF GIANT RESONANCES IN 5 8Ni R. KLEIN, Y. KAWAZOE 1 Max.Planck-Institut ffir Kernphysik, D-6900 Heidelberg, Germany P. GRABMAYR, G.J. WAGNER Physikalisches lnstitut der Universitdt Tiibingen, D-7400 Tfibingen, Germany and J. FRIEDRICH and N. VOEGLER lnstitut ffir Kernphysik der Universitdt Mainz, D-6500 Mainz, Germany Received 6 June 1984
Response functions for inelastic electron scattering from 58Ni have been determined for momentum transfers ofq ~0.4-2 fm-1. A multipole decomposition of the full continuum for excitation energies below 35 MeV yields new features of the E1 and E3 strengths. The E2 strength is in excellent agreement with a-scattering data which demonstrates the usefulness of both probes and shows the isospin purity of the isoscalar giant quadrupole resonance.
Given the complexity of nuclear response functions in the giant resonance region, knowledge of giant resonances cannot be claimed unless compatibility of giant resonance excitation by different probes has been achieved. In 208pb ' strengths of the isoscalar giant quadrupole resonance (GQR) exhausting ~30%, ~80% and ~70% of the energy weighted sum rule (EWSR) have been deduced from low- [1] and highenergy [2] electron scattering and from hadron scattering experiments (ref. [3] and references therein), respectively. To some extent these discrepancies may result from background subtractions: while the background problems of hadron scattering experiments are notorious, the radiative tail of electron scattering spectra is calculable in principle, in practice, however, it is quite c o m m o n to subtract an empirical background as well (e.g. refs. [ 1,4] ). To study the compatibihty o f electron and hadron scattering experiments we chose the target nucleus 58Ni where also results obtained with various probes are available for comparison (ref. [4] and references 1 On leave of absence from Tohoku University, Sendai, Japan.
therein, refs. [ 5 - 7 ] ) . Furthermore radiative corrections are smaller than in 2°spb; we believe that they can be calculated with an accuracy permitting a meaningful interpretation of the corrected strength as nuclear response function. Ten (e, e') spectra covering excitation energies up to about 50 MeV were taken with a 50 mg/cm 2 isotopically enriched 58Ni target for elastic momentum transfers qel ~ 0 . 4 - 2 fm - 1 using beams of 124, 180 and 300 MeV electrons from the Mainz linear accelerator [8]. With the 180 ° spectrometer [8] an overall energy resolution of zXE/E < 10 - 3 was achieved. The resulting spectroscopic information on bound states has been published previously [9] * 1. In this letter we concentrate on the analysis o f the giant resonance region. Good counting statistics, a large range of momentum transfer and the absence o f instrumental background enabled us to perform a multipole analysis of the full continuum in 1 MeV wide bins. This procedure introduces much less bias than the B r e i t ,1 The 5.903 MeV group reported there turned out to be an unresolved multiplet of states. We take the opportunity to withdraw the 1(-) assignment and the B(E1) value. 25
Volume 145B, number 1,2
PHYSICS LETTERS i
Fig. 1. shows a spectrum taken at qel = 0.91 fm - 1 i.e. close to the maximum of the E3 form factor. Radiative corrections were calculated with an updated version o f the program described in ref. [2] using elastic form factors. The vanishing of count rates in between discrete states in the unfolded spectrum serves a a performance test and gives us confidence also for the giant resonance region, where the radiative corrections amount to less than 15% for q > 0.7 f m - 1. The response function W(q, ~) defined as d2o/dg2 dco divided b y the Mott cross section was decomposed into form factors FL(q) o f multipolarity L 6
i
58Ni(e.e') 150
E0=180MeV O =600
#, >=
~ 50
20
,tO
Ex
13 September 1984
[MeV]
W(q, co)= ~
Fig. 1. Spectrum of the SaNi(e, e') reaction for qel = 0.91 fm -1 with and without radiative unfolding (lower and upper curve, respectively). The (presumably isovector) giant octupole resonance near 13 MeV and the giant dipole plus quadrupole resonances around 16 MeV are clearly visible. The slight enhancement around 30 MeV is a reminiscence of a quasi-free scattering peak with strength contributions from several multipoles.
L=I
SL(CO) • IFL(q)l 2 ,
by a least-squares fitting procedure applied to determine the multipole strengths SL(CO). The q-dependence of the form factors was calculated with the DWBA program HADES [ 10] using Tassie transition densities based on the ground-state charge density from ref. [11]. (The same charge density was also used to calculate the radial moments required for the evaluation of the EWSRs leading to substantial dif-
Wigner peak fitting procedure following an empirical background subtraction which was applied e.g. in ref. [4].
58Ni(e, e') .q
I
00
Ex = 12 -13 MeV
i "
I
I
Ex =17- 18MeV
~
o
blC::
EII~
"01 "10 100 X
•
o
5
10
I
J
.5
1.0
.5
1.0 1.5 qeff/fm-1
2.0
.5
I
I
I
1.0
1.5
2.0
Fig. 2. Reduced cross sections for bound states of known spins and parities (left) and for energy bins where E3 strength (centre) and E2 strength (right) dominate. The latter are decomposed into DWBA form factors based on Tassie transition densities. Only full dots were included in the least-squares fit for L ~< 3 strength. Because of uncertainties in the shapes of the form factors we do not attribute the additional strengths at high q-values to multipolarities with L ~ 4. 26
Volume 145B, number 1,2
PHYSICS LETTERS
ferences with the sum rule values used in ref. [4]. These form factors yield excellent fits for low-lying collective states (see fig. 2 left). Their use in the giant resonance region, however, must be taken as one of several approximations of our method. (i) The factorization in eq. (1) is an essential assumption. A recent investigation of an RPA model response function shows that the ansatz is justified for small momentum transfers including the first maximum of the form factors [12]. (ii) Tassie form factors are exact for extremely collective states exhausting the full EWSR or if the doorway dominance scheme is valid [13]. In the opposite extreme of single-particle transitions, we have performed calculations in a continuum shell model without residual interactions in the spirit of ref. [14]. These calculations show that for excitation energies below 25 MeV the Tassie form factors represent a fair approximation also for high L-values which are the least collective in nature. (ii) Transverse excitations are neglected for the sake of simplicity. The maximum scattering angle was 85 ° and, in fact, in the bound-state region [9] no signature for transverse excitation was observed. Furthermore, the continuum shell model calculations [14] indicate that less than 15% of the total cross section is of transverse nature even at the maximum scattering angle. Therefore we believe that the approximations warrant reliable results in the low-L (L ~< 3), low-co (co < 30 MeV) and low-q (q < 1.3 fm - 1 ) region. For the energy bins at 12.5 and 17.5 MeV the decompositions are shown in fig. 2 (centre and right). B(EL) values per MeV resulting from the fitting procedure are presented for L = 1,2 and 3 in fig. 3. The error bars denote uncorrelated statistical errors. The E1 strength distribution exhibits a clear picture of the giant dipole resonance (GDR). Comparison with photonuclear results [15] shows good agreement in absolute magnitude and shape in the peak and the high-energy slope. However, we observe in addition a low-energy component at about 12 MeV which evades observation in photonuclear processes due to threshold effects. This component is also visible but less pronounced in ref. [4] and also in earlier electron scattering work [16] but was interpreted [17] as GQR. We feel that in the light of the present result the discussion on the isospin splitting o f the GDR (see e.g. ref. [18]) should be resumed.
13 September 1984 i
I
'
I
'
I
'
58Ni(e, e')
2.0
E1
~----,1.5
E
~ 1.0 IJ.l
0.5 --~l. 3
200
[
~1501
12~
•100H[
10w
,,,5011~ c~.~'~,~/
8~o -o "o
6b
10]-~1" 'tn
~
E3
-
2
1.1.1
No
0
10
20 30 40 Ex [MeV] Fig. 3. Strength distributions (histograms) with uncor[elated statistical error bars. The E1 strength is compared to results from photonuclear reactions [15]. The comparison of the E2 strength with an (c~,a') spectrum [6] (right hand scale, suppressed zero point) shows agreement in shape and magnitude (see text) for the isoscalar GQR riding on a smooth "background" (dashed line) assumed in the (a, c/) analysis.
The E2 strength shows a GQR at about 16 MeV on top of a smooth continuous E2 distribution. The latter may contain some E0 strength which is indistinguishable with the present method and which is known to lack concentration [19]. The GQR structure on top of the dashed line exhausts 26% of the electromagnetic EWSR. For comparison we also show in fig. 3 an (a, ~') spectrum [6] taken at 01a b = 11 °, i.e. in a maximum of the L = 2 angular distribution. The comparison is absolute: the (55 -+ 15)% of the isoscalar E2 EWSR known from (a, a') experiments 27
Volume 145B, number 1,2
PHYSICS LETTERS
[20] to reside in the resonance structure (above the dashed line) was converted into B(E2) values. The excellent agreement of the GQR properties determined with isoscalar and electromagnetic probes makes us confident that the problems occurring in the analysis have been dealt with appropriately. And then, as a result, the agreement shows a high degree of isospin purity of the GQR which contrasts to the isospin impurity of the GQR in 118Sn reported recently [21]. Since only ~55% of the isoscalar EWSR is exhausted by the GQR proper, part of the continuous E2 strength underneath the GQR is likely to be of isoscalar nature too. Such smoothly distributed strength cannot be unraveled from the background in hadron scattering experiments. Our data do not confirm the existence of an isovector GQR at about 32 MeV reported by ref. [4]. The E3 strength distribution exhibits a fragmented isoscalar low-energy octupole resonance below 10 MeV which exhausts 16% of the isoscalar EWSR and a second E3 resonance near 13 MeV which is presumably of isovector nature because it was not observed in any a-scattering experiment. It exhausts ~28% of the isovector EWSR. As the analysis at the high momentum transfers is particularly dependent on the assumptions about the shape of the form factors, we conclude only very tentatively that the missing E3 strength resides above 35 MeV excitation energy. In summary, in addition to new information on giant dipole and octupole resonances in 58Ni the present work exhibits excellent agreement of GQR properties studied by electrons and a-particles, re-
28
13 September 1984
spectively. In view of the difficulties mentioned above this agreement is far from being trivial.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10[ [11] [12]
[13] [ 14] [15] [16] [17] [ 18] [19] [20] [21]
G. Kfihner et al., Phys. Lett. 104B (1981) 189. M. Sasao and Y. Torizuka, Phys. Rev. C15 (1977) 217. H.P. Morsch et al., Phys. Rev. C28 (1983) 1947. R. Pitthan et al., Phys. Rev. C21 (1980) 147. M.T. Collins, C.C. Chang, S.L. Tabor, G.J. Wagner and J.R. Wu, Phys. Rev. Lett. 42 (1979) 1440. K.T. Kn6pfle et al., J. Phys. (NY) G7 (1981) L99. B. Donin et al., Contributed paper HESANS 83 (Orsay) p. 31. H. Ehrenberg et al., Nucl. Instrum. Methods 105 (1972) 253. R. Klein et al., Nuovo Cimento 76A (1983) 369. H.G. Andresen, private communication. C.W. de Jager, H. de Vries and C. de Vries, At. Data Nucl. Data Tables 14 (1974) 491. J. Decharg~, D. Gogny, B. Grammaticos and L. Sips, Phys. Rev. Lett. 49 (1982) 982; D. Gogny, private communication. T.J. Deal and S. Fallieros, Phys. Rev. C7 (1973) 1709; G.F. Bertsch, Phys. Rev. C10 (1974) 933. Y. Kawazoe, G. Takada and H. Matsuzaki, Prog. Theor. Phys. 54 (1975) 1394. S.C. Fultz, R.A. Alvarez, B.L. Berman and P. Meyer, Phys. Rev. C10 (1971) 608. I.S. Gul'karov et al., Sov. J. Nucl. Phys. 9 (1969) 274. V.M. Khvastunov et al., S ov. J. Nucl. Phys. 25 (1977) 491. E.M. Diener, J.F. Amann, P. Paul and S.L. Blatt, Phys. Rev. C3 (1971) 2303. U. Garg et al., Phys. Rev. C25 (1982) 3204. D.H. Youngblood et al., Phys. Rev. C23 (1981) 1997. J.L. Ullmann et al., Phys. Rev. Lett. 51 (1983) 1038.