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The GDR width in hot Sn nuclei
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A649 (1999) 123c-129c
The GDR width in hot Sn nuclei M. P. Kelly~, K. A. Snover ~, J. P. S. van Schagen ", M. Kicifiska-Habiorb, Z. Trznadel u "Nuclear Physics Laboratory, University of Washington, Seattle, Washington 98195 bInstitute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland Gamma-rays, charged particles and evaporation residue products from lso+1°°Mo collisions at E(lso)=125 to 217 MeV have been measured in order to understand better the width evolution of the GDR in hot nuclei. Detailed angular distributions of all reaction products are used to determine important preequilibrium and bremsstrahlung effects and the giant-dipole parameters as a function of temperature. Results show the GDR width increasing with final-state temperature up to T=2.5 MeV, in contrast with previous works which argue for a saturation of the width in this energy range. 1. I N T R O D U C T I O N The apparent saturation of the GDR width and strength remains one of the interesting and puzzling questions in the field of hot giant resonances. GDR studies at nuclear temperatures T < 2 MeV show the width increasing rapidly with bombarding energy due to increasing spin induced deformation, and increasing thermal shape fluctuations [1,2! In this regime the global systematics of the GDR width are described reasonably well by shape fluctuation calculations in which the quadrupole deformation of the nucleus couples adiabatically to the GDR vibration (see e.g. Ref [3]). At higher bombarding energies where the angular momentum saturates it has been proposed that the GDR width should saturate. Previous experiments [2,4-7] have presented evidence for a saturating width and, at higher bombarding energies, a saturating high-energy "/-ray multiplicity (number of high energy 7-rays per compound nucleus formed) for GDR decay. However, at high bombarding energy [8] it is difficult to know the initial excitation energy of the decaying nuclei, which greatly complicates the interpretation of these experimental data. This work presents a detailed study of reaction products in 1so + l°°Mo collisions at E(lSO) = 125 to 217 MeV, spanning the interesting energy range where the GDR width is claimed to saturate. Angular distributions of preequilibrium and evaporative protons and a-particles, evaporation residues and multiplicity-gated high-energy photons have been measured. The effects of preequilibrium emission are significant in this energy range, in contrast to assumption in previous experiments. Gamma-ray angular distributions are used here to constrain the bremsstrahlung yield underlying the GDR. As a result we are able to extract with confidence the GDR parameters and the final-state temperature corresponding to GDR emission. Our results show a GDR width still increasing with temperature up to T~2.5 MeV. 0375-9474/99/$ see front matter © 1999 Publishedby Elsevier Science B.V. All rights reserved. PII S0375-9474(99)00049-4
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M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
2. E X P E R I M E N T Data were measured at the University of Washington Nuclear Physics Laboratory. Excited nuclei in the mass region of 11SSn were produced using a 125-217 MeV pulsed 1so beam from the tandem-linac accelerator incident on isotopically enriched l°°Mo targets. High-energy 7-rays were measured with a movable array of three large NaI spectrometers, and low energy 7-ray multiplicities were measured using 22 small NaI crystals covering approximately 20% of 47r. A top view of this new high-energy 7-ray apparatus is shown in fig. 1. In a separate experiment, a-particle and proton spectra were measured with three CsI detectors to determine preequilibrium particle energies and multiplicities [9]. A silicon telescope was used to measure evaporation residues. These particle and residue data were used to determine the average mass, Z, excitation energies and fusion cross sections for the populated compound nuclei.
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Fig. 1. Top view of the three large NaI spectrometers and the multiplicity filter apparatus used to measure multiplicity gated highenergy 7-ray spectra. Only 5 of the 22 multiplicity filter elements are shown.
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High energy 7-rays were separated from neutron-induced events based on the measured time-of-flight. "t-ray spectra were measured at 81ab=55°, 90 ° and 1250 and transformed to the compound nucleus center-of-mass. The form of the 7-ray angular distribution was assumed to be ¢r(0~m) = A0[1 + alVl(cos(0¢,,~)) + azP2(cos(0cm))], where P1 and P2 are Legendre Polynomials, based on the dominance of electric dipole radiation. The al(ET) coefficients, which must be zero for statistical emission, are nonzero at high E, due to bremsstrahlung emission. Perhaps surprisingly, the measured al(E~) indicates significant bremsstrahlung as low as 125 MeV bombarding energy (6.9 MeV/u).
M.P Kelly et al./Nuclear Physics A649 (1999) 123c-129c
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3. D A T A A N A L Y S I S Corrections for preequilibrium energy losses in our bombarding energy range were estimated in the following manner. First, detailed measurements of preequilibrium proton and a-particle multiplicities and kinetic energies were made at 200 MeV bombarding energy i9] in coincidence with high energy v-rays, in order to determine the preequilibrium emission in events leading to fusion. The neutron contribution was estimated using a model calculation [10]. This procedure leads to a preequilibrium energy loss of 20% of the complete fusion energy at 200 MeV. Singles proton and a-particle multiplicities were measured at 169 and 200 MeV and the preequilibrium energy loss at 169 MeV was estimated by scaling the energy loss at 200 MeV by the ratio of the measured preequilibrium singles proton and a-particle multiplicities at 169 and 200 MeV. Preequilibrium neutron losses were assumed to scale with the proton losses. The preequilibrium energy losses at 169 and 200 MeV were subtracted from the complete fusion excitation energies and these reduced excitation energies are plotted with estimated error bars in Fig. 4. A straight line fit (dashed line) shows our best estimate of the average initial excitation energy of the compound system versus Ewoj. The deduced preequilibrium energy loss as a function of projectile bombarding energy and the corresponding average excitation energy, mass, and Z of the compound nuclei formed were used as input to CASCADE. Statistical model calculations were made using a version of the code C A S C A D E and Reisdorf's [11,12] level density. Measured residue cross sections from Ref. [9] were used for the initial fusion cross sections. GDR and bremsstrahlung parameters were found by fitting simultaneously the statistical contribution plus a bremsstrahlung component to the measured 90 ° cross section and the al(E~) coefficients. The GDR contribution is well described with a single Lorentz curve for the strength function. A parameterization of the bremsstrahlung cross section as a simple exponential, with isotropic emission in a reference frame moving with 0.5vb~m has been used for nucleon-nucleon bremsstrahlung at higher bombarding energies [13]. However, this form is inadequate to describe the measured a,(E~), as shown for the case of 200 MeV bombarding energy in Fig. 2. This disagreement is observed at all bombarding energies. Bremsstrahlung at these (low) bombarding energies is not well understood theoretically so we consider empirical parameterizations. A 'curved' bremsstrahlung cross section given by ~rb. . . . =k(1-x2)~/x gives good fit results. Here x=E~/E~i,, and k, a and Elim are fit parameters. Very similar fit results are obtained with ~b. . . . . =k/(A+e E~/Ef') and v ...... =0.5vb.,m. Alternatively, one may retain the simple exponential form eb. . . . =k.e (-E~/g") and vary the source velocity from ~0.3vb~,m at E~=20 MeV to ~0.6vb~,,~ at E~=30 MeV. The fitted GDR parameters are not sensitive to the parameterization, though it is very important to include the bremsstrahlung component in the analysis. Fit results using the first parameterization are shown in Fig. 2, right panel, and in Fig. 3.
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E r (MeV) Fig. 3. Measured data a n d C A S C A D E plus bremsstrahlung fits. First row - "l-ray production cross sections. S e c o n d row - al (E~) angular distribution c o e ~ c i e n t s . Third row - divided plots.
Fig. 3 shows high-energy "/-ray spectra and al(E~) coefficients for all five bombarding energies, along with CASCADE plus bremsstrahlung fits to the region E~= 11-38 MeV. Using data from the multiphcity array, a fold>4 condition has been placed on these data. The fits are generally good for both the cross section and the a1(E~). To remove approximately the effect of the level density and display the data on a linear scale we show 'divided' plots in the 3rd row. To ensure clean 7-ray spectra a multiplicity cut was used. Since we don't have an evaporation residue tag, we use the fold_>4 multiplicity cut to ehminate non-compound nucleus background. Such background is evident in the fold_>0 data (not shown) for E ~ < l l MeV where the al(E~) is positive due to a nonequilibrium process such as "/-decay of projectile-like fragments (in this low energy region, bremsstrahlung is neghgible). There is also some background near E , = 15 MeV from decay of 12C fragments. The background is strongly suppressed by the multiphcity cut, as evidenced by the reduction of the at(E,) due to these processes. For the fold-gated data, shown in Fig. 3, al(Ex) is nearly zero on the low side of the GDR, as expected for nearly pure statistical decay in the presence of a small bremsstrahlung yield. Fits to fold>4 and fold_>0 data above 11 MeV give similar
M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
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results, indicating that any residual nonstatistical background in this E~ region is small. 4. R E S U L T S A N D D I S C U S S I O N Fig. 4 shows the energy of decaying compound nuclei produced in isO+l°°Mo reactions accounting for non-statistical and statistical energy losses. As discussed above, Ei,~it represents the initial compound nucleus excitation energy taking into account preequilibrium emission. Ei includes the additional energy lost on average by particle evaporation prior to GDR decay, calculated using CASCADE. Finally, E! represents the average thermal energy for GDR decay with ET=ED=15 MeV. E t is obtained from Ei by subtracting the gamma decay energy and the rotational energy. We note that El is small and increases more slowly with bombarding energy than does Ei~it. Note also that the GDR width and 7-ray yield will saturate with bombarding energy if this curve flattens out at higher energies. In order to interpret properly the GDR parameters, we calculate the average temperature associated with GDR decay, given by T = (dln(p)/dE) -1 evaluated at E = E f , where p is the level density. This is the temperature relevant to thermal fluctuation calculations of dipole absorption by a heated nucleus [1]. Fitted GDR strengths all lie in the range 1.1 to 1.3 times the classical dipole sum rule, similar to the value of 1.26 deduced from ground-state photoabsorption on nSSn [14]. Good agreement (within -b5%) is also found for the resonance energies compared to the ground-state GDR value. Neither S nor E0 show significant temperature dependence. These results represent the best test to date of the expectation that the strength and resonance energy of the GDR built on excited states should be the same as for the GDR built on the ground state, since all significant parameters relevant to the present determination - initial excitation energy, fusion cross section and level density parameter [15] - have been measured. The dependence of the GDR width on temperature from the present study is shown by the solid points in Fig. 5, together with results from previous fusion-evaporation experiments [16-19](open points) at lower excitation energies [20], where preequilibrium corrections are small. Where necessary we have recomputed the temperatures for the previous measurements. As can be seen in Fig. 5 the GDR width is still increasing up to T=2.5 MeV, the highest temperature reached in the present study. Also shown in Fig. 5, top panel, is the average angular momentum at the time of GDR decay for lsO+l°°Mo reactions calculated using CASCADE (a similar curve is found for the other fusion-evaporation reactions) and in the bottom panel the thermal fluctuation calculations of Kusnezov and Alhassid [3,22] calculated using the average angular momentum shown. Theoretically the width continues to increase beyond the point at which the angular momentum saturates because thermal shape fluctuations are still rising significantly with increasing T. Previous authors who have made measurements at higher excitation energies [4,5,7] have concluded from plots of deduced GDR width vs. initial excitation energy that the GDR width saturates in this energy region. However, applying our results for preequilibrium energy losses to these experiments by assuming the lost energy scales with E/A suggests larger losses than were previously assumed. Additional losses decrease the computed temperatures and raise the fitted GDR widths; the latter occurs because the spectra must be refit with CASCADE at a lower initial excitation energy. We have computed the
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M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
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Tf(MeV) Fig. 5. Top panel - average angular momentum for GDR decay in lsO+l°°Mo. Bottom panel -measured GDR widths for decay of Sn and nearby mass compound nuclei. Solid line Thermal fluctuation calculation of ref.[22]. -
temperatures and estimated the width corrections for some of these data [4,5]; the results for T --- 2.5 to 3 MeV are widths that are increasing more rapidly than one would expect from a smooth extrapolation of the data shown in Fig. 5. However, even the uncorrected widths, as quoted in these references, together with our temperature estimates, show an increasing GDR width in the region T = 2.5 to 3 MeV [23]. 5. C O N C L U S I O N Our detailed study of GDR decay and preequilibrium emission in 1so + t°°Mo reactions populating Sn and nearby compound nuclei shows that the GDR width increases steadily with temperature up to T = 2.5 MeV. The GDR strength continues to exhaust or even exceed the dipole sum rule up to the highest energy studied. Model calculations for Sn nuclei based on the adiabatic thermal shape fluctuations of a heated rotating liquid drop account for the increase in GDR width and the magnitudes at T~2.5 MeV but exceed the data at lower energies (temperatures). In order to understand the GDR width at even higher temperatures it is essential that detailed measurements of preequilibrium losses be carried out in order to determine the properties, particularly the excitation energy, of the decaying nuclei. REFERENCES
1. K.A. Snover, Ann. Rev. Nucl. Part. Sci. 36, 545 (1986). 2. J.J. Gaardhoje, Ann. Rev. Nucl. Part. Sci. 42, 483 (1992). 3. D. Kusnezov, Y Alhassid, and K.A. Shover, Phys. Rev. Lett. 81,542 (1998).
M.P Kelly et al./Nuclear Physics A649 (1999) 123c-129c
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4. A. Bracco, et al., Phys. Rev. Lett. 62, 2080 (1989). 5. H.J. Hofmann, J.C. Bacelar, M.N. Harekeh, T.D. Poelhekken, A. van der Woude Nuc. Phys. A571, 301 (1994). 6. D. Pierroutsakou, et al., Nuc. Phys. A600, 131 (1996). 7. G. Enders, et al., Phys. Rev. Lett. 69, 249 (1992). 8. J.H. Le Faou et al., Phys. Rev. Lett. 72, 3321 (1994). 9. MP. Kelly, J.F. Liang, A.A. Sonzogni, K.A. Shover, J.P.S. van Schagen, J.P. Lestone Phys. Rev. C 56, 3201 (1997). 10. J. Randrup and R. Vandenbosch, Nucl. Phys. A474, 219 (1987). 11. W. Reisdorf, Z. Phys. A 300 (1981). 12. M. Kicinska-Habior, K.A. Shover, C.A. Gossett, J.A. Behr, G. Feldman, H.K. Glatzel J.H. Gundlach, E.F. Garman, Phys. Rev. C 36,612 (1987). 13. H. Nifennecker and J.A. Pinston, Ann. Rev. Nucl. Part. Sci. 40, 113 (1990). 14. A. Lepretre, H. Bell, R. Bergere, P. Carlos, A. De Miniac, A. Veyssiere, Nucl. Phys. A219, 39 (1974). 15. G. Nebbia et al., Nuc. Phys. A578, 285 (1994). 16. J.J. Gaardhoje, C. Ellegaard, B. Herskind, S.G. Steadman. Phys. Rev. Let. 53, 148 (1984). 17. J.J. Gaardhoje, C. Ellegaard, B. Herskind, R.M. Diamond, M.A. Deleplanque, G. Dines, A.O. Macchiavelli, F.S. Stephens, Phys. Rev. Let. 56, 1783 (1986). 18. D.R. Chakrabarty, S. Sen, M. Thoennessen, N. Alamanos, P. Paul, R. Schicker, Phys. Rev. C 36, 1886 (1987). 19. K.A. Snover, AIP Conference Proceedings 259, 299 (1992). 20. Inelastic scattering results from ref. [21] exhibit a trend similar to the data shown in Fig. [5]. 21. E. Ramakrishnan, et al., Phys. Rev. Let. 76, 2025 (1996). 22. D. Kusnezov, private communication. 23. We don't include the results of ref. [7] since we don't know how to estimate preequilibrium losses for deep inelastic scattering.
Nuclear Physics A649 (1999) 123c-129c
The GDR width in hot Sn nuclei M. P. Kelly~, K. A. Snover ~, J. P. S. van Schagen ", M. Kicifiska-Habiorb, Z. Trznadel u "Nuclear Physics Laboratory, University of Washington, Seattle, Washington 98195 bInstitute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland Gamma-rays, charged particles and evaporation residue products from lso+1°°Mo collisions at E(lso)=125 to 217 MeV have been measured in order to understand better the width evolution of the GDR in hot nuclei. Detailed angular distributions of all reaction products are used to determine important preequilibrium and bremsstrahlung effects and the giant-dipole parameters as a function of temperature. Results show the GDR width increasing with final-state temperature up to T=2.5 MeV, in contrast with previous works which argue for a saturation of the width in this energy range. 1. I N T R O D U C T I O N The apparent saturation of the GDR width and strength remains one of the interesting and puzzling questions in the field of hot giant resonances. GDR studies at nuclear temperatures T < 2 MeV show the width increasing rapidly with bombarding energy due to increasing spin induced deformation, and increasing thermal shape fluctuations [1,2! In this regime the global systematics of the GDR width are described reasonably well by shape fluctuation calculations in which the quadrupole deformation of the nucleus couples adiabatically to the GDR vibration (see e.g. Ref [3]). At higher bombarding energies where the angular momentum saturates it has been proposed that the GDR width should saturate. Previous experiments [2,4-7] have presented evidence for a saturating width and, at higher bombarding energies, a saturating high-energy "/-ray multiplicity (number of high energy 7-rays per compound nucleus formed) for GDR decay. However, at high bombarding energy [8] it is difficult to know the initial excitation energy of the decaying nuclei, which greatly complicates the interpretation of these experimental data. This work presents a detailed study of reaction products in 1so + l°°Mo collisions at E(lSO) = 125 to 217 MeV, spanning the interesting energy range where the GDR width is claimed to saturate. Angular distributions of preequilibrium and evaporative protons and a-particles, evaporation residues and multiplicity-gated high-energy photons have been measured. The effects of preequilibrium emission are significant in this energy range, in contrast to assumption in previous experiments. Gamma-ray angular distributions are used here to constrain the bremsstrahlung yield underlying the GDR. As a result we are able to extract with confidence the GDR parameters and the final-state temperature corresponding to GDR emission. Our results show a GDR width still increasing with temperature up to T~2.5 MeV. 0375-9474/99/$ see front matter © 1999 Publishedby Elsevier Science B.V. All rights reserved. PII S0375-9474(99)00049-4
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M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
2. E X P E R I M E N T Data were measured at the University of Washington Nuclear Physics Laboratory. Excited nuclei in the mass region of 11SSn were produced using a 125-217 MeV pulsed 1so beam from the tandem-linac accelerator incident on isotopically enriched l°°Mo targets. High-energy 7-rays were measured with a movable array of three large NaI spectrometers, and low energy 7-ray multiplicities were measured using 22 small NaI crystals covering approximately 20% of 47r. A top view of this new high-energy 7-ray apparatus is shown in fig. 1. In a separate experiment, a-particle and proton spectra were measured with three CsI detectors to determine preequilibrium particle energies and multiplicities [9]. A silicon telescope was used to measure evaporation residues. These particle and residue data were used to determine the average mass, Z, excitation energies and fusion cross sections for the populated compound nuclei.
/
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Fig. 1. Top view of the three large NaI spectrometers and the multiplicity filter apparatus used to measure multiplicity gated highenergy 7-ray spectra. Only 5 of the 22 multiplicity filter elements are shown.
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High energy 7-rays were separated from neutron-induced events based on the measured time-of-flight. "t-ray spectra were measured at 81ab=55°, 90 ° and 1250 and transformed to the compound nucleus center-of-mass. The form of the 7-ray angular distribution was assumed to be ¢r(0~m) = A0[1 + alVl(cos(0¢,,~)) + azP2(cos(0cm))], where P1 and P2 are Legendre Polynomials, based on the dominance of electric dipole radiation. The al(ET) coefficients, which must be zero for statistical emission, are nonzero at high E, due to bremsstrahlung emission. Perhaps surprisingly, the measured al(E~) indicates significant bremsstrahlung as low as 125 MeV bombarding energy (6.9 MeV/u).
M.P Kelly et al./Nuclear Physics A649 (1999) 123c-129c
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3. D A T A A N A L Y S I S Corrections for preequilibrium energy losses in our bombarding energy range were estimated in the following manner. First, detailed measurements of preequilibrium proton and a-particle multiplicities and kinetic energies were made at 200 MeV bombarding energy i9] in coincidence with high energy v-rays, in order to determine the preequilibrium emission in events leading to fusion. The neutron contribution was estimated using a model calculation [10]. This procedure leads to a preequilibrium energy loss of 20% of the complete fusion energy at 200 MeV. Singles proton and a-particle multiplicities were measured at 169 and 200 MeV and the preequilibrium energy loss at 169 MeV was estimated by scaling the energy loss at 200 MeV by the ratio of the measured preequilibrium singles proton and a-particle multiplicities at 169 and 200 MeV. Preequilibrium neutron losses were assumed to scale with the proton losses. The preequilibrium energy losses at 169 and 200 MeV were subtracted from the complete fusion excitation energies and these reduced excitation energies are plotted with estimated error bars in Fig. 4. A straight line fit (dashed line) shows our best estimate of the average initial excitation energy of the compound system versus Ewoj. The deduced preequilibrium energy loss as a function of projectile bombarding energy and the corresponding average excitation energy, mass, and Z of the compound nuclei formed were used as input to CASCADE. Statistical model calculations were made using a version of the code C A S C A D E and Reisdorf's [11,12] level density. Measured residue cross sections from Ref. [9] were used for the initial fusion cross sections. GDR and bremsstrahlung parameters were found by fitting simultaneously the statistical contribution plus a bremsstrahlung component to the measured 90 ° cross section and the al(E~) coefficients. The GDR contribution is well described with a single Lorentz curve for the strength function. A parameterization of the bremsstrahlung cross section as a simple exponential, with isotropic emission in a reference frame moving with 0.5vb~m has been used for nucleon-nucleon bremsstrahlung at higher bombarding energies [13]. However, this form is inadequate to describe the measured a,(E~), as shown for the case of 200 MeV bombarding energy in Fig. 2. This disagreement is observed at all bombarding energies. Bremsstrahlung at these (low) bombarding energies is not well understood theoretically so we consider empirical parameterizations. A 'curved' bremsstrahlung cross section given by ~rb. . . . =k(1-x2)~/x gives good fit results. Here x=E~/E~i,, and k, a and Elim are fit parameters. Very similar fit results are obtained with ~b. . . . . =k/(A+e E~/Ef') and v ...... =0.5vb.,m. Alternatively, one may retain the simple exponential form eb. . . . =k.e (-E~/g") and vary the source velocity from ~0.3vb~,m at E~=20 MeV to ~0.6vb~,,~ at E~=30 MeV. The fitted GDR parameters are not sensitive to the parameterization, though it is very important to include the bremsstrahlung component in the analysis. Fit results using the first parameterization are shown in Fig. 2, right panel, and in Fig. 3.
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M.P. Kelly et a l . / N u c l e a r Physics A 6 4 9 (1999) 123c-129c
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E r (MeV) Fig. 3. Measured data a n d C A S C A D E plus bremsstrahlung fits. First row - "l-ray production cross sections. S e c o n d row - al (E~) angular distribution c o e ~ c i e n t s . Third row - divided plots.
Fig. 3 shows high-energy "/-ray spectra and al(E~) coefficients for all five bombarding energies, along with CASCADE plus bremsstrahlung fits to the region E~= 11-38 MeV. Using data from the multiphcity array, a fold>4 condition has been placed on these data. The fits are generally good for both the cross section and the a1(E~). To remove approximately the effect of the level density and display the data on a linear scale we show 'divided' plots in the 3rd row. To ensure clean 7-ray spectra a multiplicity cut was used. Since we don't have an evaporation residue tag, we use the fold_>4 multiplicity cut to ehminate non-compound nucleus background. Such background is evident in the fold_>0 data (not shown) for E ~ < l l MeV where the al(E~) is positive due to a nonequilibrium process such as "/-decay of projectile-like fragments (in this low energy region, bremsstrahlung is neghgible). There is also some background near E , = 15 MeV from decay of 12C fragments. The background is strongly suppressed by the multiphcity cut, as evidenced by the reduction of the at(E,) due to these processes. For the fold-gated data, shown in Fig. 3, al(Ex) is nearly zero on the low side of the GDR, as expected for nearly pure statistical decay in the presence of a small bremsstrahlung yield. Fits to fold>4 and fold_>0 data above 11 MeV give similar
M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
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results, indicating that any residual nonstatistical background in this E~ region is small. 4. R E S U L T S A N D D I S C U S S I O N Fig. 4 shows the energy of decaying compound nuclei produced in isO+l°°Mo reactions accounting for non-statistical and statistical energy losses. As discussed above, Ei,~it represents the initial compound nucleus excitation energy taking into account preequilibrium emission. Ei includes the additional energy lost on average by particle evaporation prior to GDR decay, calculated using CASCADE. Finally, E! represents the average thermal energy for GDR decay with ET=ED=15 MeV. E t is obtained from Ei by subtracting the gamma decay energy and the rotational energy. We note that El is small and increases more slowly with bombarding energy than does Ei~it. Note also that the GDR width and 7-ray yield will saturate with bombarding energy if this curve flattens out at higher energies. In order to interpret properly the GDR parameters, we calculate the average temperature associated with GDR decay, given by T = (dln(p)/dE) -1 evaluated at E = E f , where p is the level density. This is the temperature relevant to thermal fluctuation calculations of dipole absorption by a heated nucleus [1]. Fitted GDR strengths all lie in the range 1.1 to 1.3 times the classical dipole sum rule, similar to the value of 1.26 deduced from ground-state photoabsorption on nSSn [14]. Good agreement (within -b5%) is also found for the resonance energies compared to the ground-state GDR value. Neither S nor E0 show significant temperature dependence. These results represent the best test to date of the expectation that the strength and resonance energy of the GDR built on excited states should be the same as for the GDR built on the ground state, since all significant parameters relevant to the present determination - initial excitation energy, fusion cross section and level density parameter [15] - have been measured. The dependence of the GDR width on temperature from the present study is shown by the solid points in Fig. 5, together with results from previous fusion-evaporation experiments [16-19](open points) at lower excitation energies [20], where preequilibrium corrections are small. Where necessary we have recomputed the temperatures for the previous measurements. As can be seen in Fig. 5 the GDR width is still increasing up to T=2.5 MeV, the highest temperature reached in the present study. Also shown in Fig. 5, top panel, is the average angular momentum at the time of GDR decay for lsO+l°°Mo reactions calculated using CASCADE (a similar curve is found for the other fusion-evaporation reactions) and in the bottom panel the thermal fluctuation calculations of Kusnezov and Alhassid [3,22] calculated using the average angular momentum shown. Theoretically the width continues to increase beyond the point at which the angular momentum saturates because thermal shape fluctuations are still rising significantly with increasing T. Previous authors who have made measurements at higher excitation energies [4,5,7] have concluded from plots of deduced GDR width vs. initial excitation energy that the GDR width saturates in this energy region. However, applying our results for preequilibrium energy losses to these experiments by assuming the lost energy scales with E/A suggests larger losses than were previously assumed. Additional losses decrease the computed temperatures and raise the fitted GDR widths; the latter occurs because the spectra must be refit with CASCADE at a lower initial excitation energy. We have computed the
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M.P Kelly et al. /Nuclear Physics A649 (1999) 123c-129c
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Complete Fusion E (MeV) Fig. 4. Dotted line - complete fusion excitation energy for lso÷l°°Mo. Dashed line Initial compound nucleus energy Einit following preequilibrium emission. Dot-Dashed line - Average compound nucleus energy Ei prior to GDR decay with E~--- ED = 15 MeV. Solid line - Average thermal energy Ef of the compound nucleus following GDR emission.
Tf(MeV) Fig. 5. Top panel - average angular momentum for GDR decay in lsO+l°°Mo. Bottom panel -measured GDR widths for decay of Sn and nearby mass compound nuclei. Solid line Thermal fluctuation calculation of ref.[22]. -
temperatures and estimated the width corrections for some of these data [4,5]; the results for T --- 2.5 to 3 MeV are widths that are increasing more rapidly than one would expect from a smooth extrapolation of the data shown in Fig. 5. However, even the uncorrected widths, as quoted in these references, together with our temperature estimates, show an increasing GDR width in the region T = 2.5 to 3 MeV [23]. 5. C O N C L U S I O N Our detailed study of GDR decay and preequilibrium emission in 1so + t°°Mo reactions populating Sn and nearby compound nuclei shows that the GDR width increases steadily with temperature up to T = 2.5 MeV. The GDR strength continues to exhaust or even exceed the dipole sum rule up to the highest energy studied. Model calculations for Sn nuclei based on the adiabatic thermal shape fluctuations of a heated rotating liquid drop account for the increase in GDR width and the magnitudes at T~2.5 MeV but exceed the data at lower energies (temperatures). In order to understand the GDR width at even higher temperatures it is essential that detailed measurements of preequilibrium losses be carried out in order to determine the properties, particularly the excitation energy, of the decaying nuclei. REFERENCES
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