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Evaporation-residue cross sections in the 40Ca + 40Ca system
EVAPORATION-RESIDUE
13 February 1978
PHYSICS LETTERS
Volume 73B, number 2
CROSS SECTIONS IN THE 4oCa + 40Ca SYSTEM
H. DOUBRE, A. CAMP, J.C. JACMART, N. POFFfi and J.C. ROYNETTE Institut de Physique NucEaire,
BP I, 91406 Orsay, France
and J. WILCZYl&KI Institute of Nuclear Physics, Cracow, Poland
Received 30 November 1977
Evaporation-residue cross sections for the 40Ca + 40Ca system have been measured telescope. From the deduced values of the barrier and critical radii, it does not appear any influence on the fusion phenomenon.
From a study of fusion excitation functions at energies close to the Coulomb barrier one can deduce information about the effective nucleus-nucleus potential. (This information is complementary to the information available from the analysis of elastic scattering data.) At higher energies the fusion data allow to determine such useful parameters as the critical radius and the critical potential [ 11, which roughly summarize our knowledge of the system at small separation distances. At low energies and for not very heavy systems the fusion cross section is identical with the evaporationresidue (ER) cross section. Only at high excitation energy in the compound nucleus, the fission process can become competitive with emission of light particles. Therefore for all light and medium compound systems the ER cross sections at low energies can be analyzed as the fusion excitation function. As part of a study of the 4oCa t 4oCa system, we have measured ER cross sections at incident energies between one and three times the Coulomb barrier. The reasons to study this particular system have been explained elsewhere [2]. As mentioned above, these measurements provide a test of the optical-model potential determined from elastic scattering measurements [2]. According to Glas and Mosel [3], one can also expect that the tightness of the system, associated with shall effects, may manifest itself in decreasing the
with a position-sensitive E-AL? that the shell closure in 40Ca has
radius parameters as compared with neighboring systems. Such a comparison could give some information on the role of the individual nucleons in the fusion process. Finally, recent microscopic calculations for collisions between closed-shell nuclei have been performed. Threedimensional time-dependent Hartree-Fock calculations [4] are now available for the 4oCa + 4oCa system, and the fusion cross sections can be compared with them. The experimental data were taken between 107 and 195 MeV incident energy (lab) in steps of about 5 MeV at the MP tandem, and at 300 MeV at the accelerator Alice of the Institut de Physique NuclCaire, Orsay. A AE-E telescope was used, at 57 cm from the 60 pg/cm2 natural Ca target evaporated on a 5 pg/cm2 carbon backing. The E-detector was a 14 X 50 mm2 solid-state detector situated inside the gas volume of the AE ionisation chamber. A 33 pg/cm2 formvar foil was used as an entrance window of the ionization chamber. With low-energy (~Einc/2 = l-4 MeV per nucleon) evaporation residues (Z 233), the AE-E techniques does not allow to determine the individual atomic number of the products but the identification of the whole group of evaporation residues was absolutely unambiguous. It was checked that the carbon backing introduced no contamination in the AE-E spectrum where the evaporation residues were observed. 135
Volume
73B, number
PHYSICS
2
I
1000
5cn
I
,’ ,’
50-Fig. with [2]) [5]).
60
70
&I
--
90-
Ecm
lM
1. Comparison of the evaporation-residue cross section the predictions of an absorbing potential (full line, ref. and of a much more transparent one (dashed line, ref. At 150 MeV, the cross section is 720 + 50 mb.
An accurate and continuous control of the beam direction is essential in measurements of the ER cross section. A reliable determination of this direction was added to the usual (left-right) checks. We used a multi-slit entrance window of the ionisation chamber, each slit having a width of OS”, separated from each other by lo. The time difference between the E and AE signals gives the localisation information which allows for simultaneous measurements at five angles. One obtains the correct position (? 0.1”) of the counter with respect to the beam by comparing the number of elastic counts for all five neighboring angles because of the strong angular dependence of the slope of the elastic cross section. The main uncertainty in the total cross section is then introduced by the extrapolation of the angular distribution to very forward angles. This extrapolation was performed by fitting the angular distribution by an analytic expression with three parameters varying smoothly with energy. The ER cross section, plotted as a function of energy, is compared in fig. 1 with the reaction cross section calculated from the optical-model potential that fits the elastic scattering data over a large energy range [2]. The agreement is rather good at low energies (up to 70 MeV cm). It has been experimentally observed [2] at these energies that inelastic scattering to the 3excited state of 4uCa is the only reaction channel which is open with a non-negligible cross section. The more transparent potential determined by Richter et al. [5] from elastic scattering data taken at E, = 136
13 February
LETTERS
1978
50-60 MeV predicts (fig. 1) a reaction cross section lower by about 120 mb than the ER cross section. At energies above 75 MeV, a number of different channels open up, since the cross section saturates at about 1000 mb and does not follow any longer the increasing reaction cross section. Obviously, these channels must be related to the so-called strongly relaxed processes which have been observed [6] to appear at about the same energy. Another process can also compete with evaporation, namely fission of the compound nucleus which would yield products of mass numbers close to 40. Though an accurate prediction of the fusion-fission cross section in the framework of the liquid-drop model [7] would require a good knowledge of the masses in the vicinity of the compound nucleus 8oZr, reasonable evaluations as well as results from the code ALICE [7] make clear that fission is negligible at cm energies below 100 MeV. This is in agreement with the recently proposed analysis [6] of 4oCa +40Ca strongly relaxed collisions at E,, = 130 MeV. Specifically, it has been shown that, at this energy, fast reactions (strongly focussed in mass and angle distributions) are accompanied by much slower processes, undistinguishable from fission because of their broad mass distribution and isotropic angular distribution. Data have been collected at 90, 100, 115, 130 and 145 MeV cm incident energy, and the latter component is not present at the two lowest energies. On the other hand it is very likely that the difference observed (fig. 2) between the ER cross section (720 mb) at 150 MeV (cm) and the expected value of the fusion cross section (’ 1100 mb, see below) is due to compound-nucleus fission. The “fission-like” [6] cross section at 130 MeV was found to be 320 mb. Predictions for the 4oCa t4uCa fusion cross section were given by Glas and Mosel [3], who have used the concepts of critical radius and critical potential. In that framework, the fusion cross section is expected to depend linearly on the quantity E-l, with different slope in the energy ranges below and above the critical energy E,: ~=nRi(l-vn/E)
when EGE,,
u = nR,2( 1 - VJE)
when E>E,,
where R, and R, are the barrier and critical radii, respectively, and VB and V, the corresponding values of the ion-ion potential. On fig. 2, the ER cross section
Volume
73B. number
2
PHYSICS
0°15
l/E,,,,
oo1i5(k”.‘)
Fig. 2. Evaporation-residue cross section as a function of E&. The predictions of Glas and Mosel [ 3 ] are given by the thin line and the dashed line, for an “average” and a “magic” system, respectively. The dashed-dotted line gives the prediction of ref. [lo] and the long-dashed line gives that of ref. [ 91. The thick full line results from a fit using the Glas and Mosel formula.
is plotted as a function of E-l and it is compared to the best fit of the model of Glas and Mosel, obtained with the following parameters VB = 5 1.5 f 0.5 MeV, R,= 10.2kO.5 fm,roB= 1.49 f 0.07 fm, I’, = 24.0 ?I 0.5MeV,Rc=6.65~0.5fm,r0c=0.97~0.07fm.The fusion barrier VB compares well with the value V, = 52.7 + 0.8 MeV determined from our earlier elastic scattering measurements [2]. It is also interesting to note that Glas and Mosel correctly predict a positive value for the critical potential. This classifies the system definitely among the “heavy” ones (light systems have a negative critical potential). However, the value of the fusion barrier suggested in ref. [3] is too high, and the predictions consequently underestimate the ER cross section. One can also notice good agreement between the value of the reduced critical radius and the one (rot = 1.OO+ 0.07 fm) used since the work by Galin et al. [l]. One then can ask whether the fusion of the 4oCa + 4oCa system gives evidence for the closed-shell structure of the colliding nuclei. The answer is clearly negative. From our analysis of the data in the framework of the Glas and Mosel model, both the critical radius and the barrier radius for the 4oCa +40Ca system do not show any deviation from the values obtained for other (non-magic) systems. A similar conclusion is drawn from a recent analysis [S] of the near-to-barrier
LETTERS
13 February
1978
fusion excitation functions for many different systems, including the 4oCa t 4oCa data. The effective nucleusnucleus potential required to reproduce these data follows the macroscopic systematics of many different systems. Such a conclusion is important for a physical interpretation of the concept of critical radius [3]. From the single-particle spectrum of the two-center shell model, as a function of the center separation, Glas and Mosel observe that energy losses can only occur at level crossings. The location of the lowest one would correspond to the critical radius, and it is expected to depend strongly on the structure of the colliding nuclei. Since the analysis of the 40Ca + 4oCa fusion data does not confirm this hypothesis (see the two variants of the Glas and Mosel predictions in fig. 2) one can suppose that the level crossing concept, based on adiabatic calculations, is not sufficient to deduce the microscopic phenomena which are responsible for dissipative processes in heavy-ion reactions. Perhaps fast collective and single-particle excitations provide the first step in overcoming the shell gap before adiabatic effects (such as level crossings) could play a role. These remarks are also valid in connection with the results of a three-dimensional time-dependent HartreeFock calculation by Bonche et al. [4 1. Even if they reproduce the shape of the excitation function, the fusion barrier is obtained at too high energy. Bonche et al. attribute this discrepancy to two reasons: (i) the force used in the calculation and (ii) the imposed spinisospin degeneracy, (i.e. four particles occupying the same spatial orbit). As a result, only 4p-4h excitations are available, and energy dissipation could consequently be underestimated. It should be noticed that the microscopic calculations (which take into account the shell closure of 4%Za) yield an interaction barrier which is too high as compared with the experimental results. On the contrary, macroscopic estimates [9,10] in which the structure of 4oCa is neglected are much more satisfying. These latter estimates have been reported in fig. 2. To summarize, the measurement of the ER cross sections for the 4oCa + 4oCa system, for energies up to three times the Coulomb barrier, is presented and a very efficient experimental method described. No evidence for a specific behavior of the system associated with the shell closure of 4oCa is found. On the contrary, the data indicate that the excitation processes 137
Volume 73B, number 2
PHYSICS LETTERS
(usually referred to as friction) are sufficiently strong to destroy the specific structure of the colliding nuclei already
in the first stages of the collision.
We would like to thank Prof. D.H.E. Gross for several stimulating of this results
discussions
and for communication
prior to publication.
References [l] J. Galin, D. Guerreau, M. Lefort and X. Tarrago, Phys. Rev. C9 (1974) 1081.
138
13 February 1978
[2] H. Doubre et al., Phys. Rev. Cl5 (1977) 693. [3] D. Glas and U. Mosel, Nucl. Phys. A237 (1975) 429. [4] P. Bonche, B. Grammaticos and S.E. Koonin, submitted to Phys. Rev. C. [S] M. Richter et al., Nucl. Phys. A278 (1977) 163. [6] J.C. Roynette et al., Phys. Lett. 67B (1977) 395, and to be published. [ 71 F. Plasil and M. Blann, Phys. Rev. Cl 1 (1975) 508. [8] K. Siwek-Wilczyfiska and J. Wilczyliski, to be published. [9] D.H.E. Gross and H. Kalinowski, private communication. [lo] K. Siwek-Wilczytiska and J. WilczyAski, Nucl. Phys. A264 (1976) 115.
13 February 1978
PHYSICS LETTERS
Volume 73B, number 2
CROSS SECTIONS IN THE 4oCa + 40Ca SYSTEM
H. DOUBRE, A. CAMP, J.C. JACMART, N. POFFfi and J.C. ROYNETTE Institut de Physique NucEaire,
BP I, 91406 Orsay, France
and J. WILCZYl&KI Institute of Nuclear Physics, Cracow, Poland
Received 30 November 1977
Evaporation-residue cross sections for the 40Ca + 40Ca system have been measured telescope. From the deduced values of the barrier and critical radii, it does not appear any influence on the fusion phenomenon.
From a study of fusion excitation functions at energies close to the Coulomb barrier one can deduce information about the effective nucleus-nucleus potential. (This information is complementary to the information available from the analysis of elastic scattering data.) At higher energies the fusion data allow to determine such useful parameters as the critical radius and the critical potential [ 11, which roughly summarize our knowledge of the system at small separation distances. At low energies and for not very heavy systems the fusion cross section is identical with the evaporationresidue (ER) cross section. Only at high excitation energy in the compound nucleus, the fission process can become competitive with emission of light particles. Therefore for all light and medium compound systems the ER cross sections at low energies can be analyzed as the fusion excitation function. As part of a study of the 4oCa t 4oCa system, we have measured ER cross sections at incident energies between one and three times the Coulomb barrier. The reasons to study this particular system have been explained elsewhere [2]. As mentioned above, these measurements provide a test of the optical-model potential determined from elastic scattering measurements [2]. According to Glas and Mosel [3], one can also expect that the tightness of the system, associated with shall effects, may manifest itself in decreasing the
with a position-sensitive E-AL? that the shell closure in 40Ca has
radius parameters as compared with neighboring systems. Such a comparison could give some information on the role of the individual nucleons in the fusion process. Finally, recent microscopic calculations for collisions between closed-shell nuclei have been performed. Threedimensional time-dependent Hartree-Fock calculations [4] are now available for the 4oCa + 4oCa system, and the fusion cross sections can be compared with them. The experimental data were taken between 107 and 195 MeV incident energy (lab) in steps of about 5 MeV at the MP tandem, and at 300 MeV at the accelerator Alice of the Institut de Physique NuclCaire, Orsay. A AE-E telescope was used, at 57 cm from the 60 pg/cm2 natural Ca target evaporated on a 5 pg/cm2 carbon backing. The E-detector was a 14 X 50 mm2 solid-state detector situated inside the gas volume of the AE ionisation chamber. A 33 pg/cm2 formvar foil was used as an entrance window of the ionization chamber. With low-energy (~Einc/2 = l-4 MeV per nucleon) evaporation residues (Z 233), the AE-E techniques does not allow to determine the individual atomic number of the products but the identification of the whole group of evaporation residues was absolutely unambiguous. It was checked that the carbon backing introduced no contamination in the AE-E spectrum where the evaporation residues were observed. 135
Volume
73B, number
PHYSICS
2
I
1000
5cn
I
,’ ,’
50-Fig. with [2]) [5]).
60
70
&I
--
90-
Ecm
lM
1. Comparison of the evaporation-residue cross section the predictions of an absorbing potential (full line, ref. and of a much more transparent one (dashed line, ref. At 150 MeV, the cross section is 720 + 50 mb.
An accurate and continuous control of the beam direction is essential in measurements of the ER cross section. A reliable determination of this direction was added to the usual (left-right) checks. We used a multi-slit entrance window of the ionisation chamber, each slit having a width of OS”, separated from each other by lo. The time difference between the E and AE signals gives the localisation information which allows for simultaneous measurements at five angles. One obtains the correct position (? 0.1”) of the counter with respect to the beam by comparing the number of elastic counts for all five neighboring angles because of the strong angular dependence of the slope of the elastic cross section. The main uncertainty in the total cross section is then introduced by the extrapolation of the angular distribution to very forward angles. This extrapolation was performed by fitting the angular distribution by an analytic expression with three parameters varying smoothly with energy. The ER cross section, plotted as a function of energy, is compared in fig. 1 with the reaction cross section calculated from the optical-model potential that fits the elastic scattering data over a large energy range [2]. The agreement is rather good at low energies (up to 70 MeV cm). It has been experimentally observed [2] at these energies that inelastic scattering to the 3excited state of 4uCa is the only reaction channel which is open with a non-negligible cross section. The more transparent potential determined by Richter et al. [5] from elastic scattering data taken at E, = 136
13 February
LETTERS
1978
50-60 MeV predicts (fig. 1) a reaction cross section lower by about 120 mb than the ER cross section. At energies above 75 MeV, a number of different channels open up, since the cross section saturates at about 1000 mb and does not follow any longer the increasing reaction cross section. Obviously, these channels must be related to the so-called strongly relaxed processes which have been observed [6] to appear at about the same energy. Another process can also compete with evaporation, namely fission of the compound nucleus which would yield products of mass numbers close to 40. Though an accurate prediction of the fusion-fission cross section in the framework of the liquid-drop model [7] would require a good knowledge of the masses in the vicinity of the compound nucleus 8oZr, reasonable evaluations as well as results from the code ALICE [7] make clear that fission is negligible at cm energies below 100 MeV. This is in agreement with the recently proposed analysis [6] of 4oCa +40Ca strongly relaxed collisions at E,, = 130 MeV. Specifically, it has been shown that, at this energy, fast reactions (strongly focussed in mass and angle distributions) are accompanied by much slower processes, undistinguishable from fission because of their broad mass distribution and isotropic angular distribution. Data have been collected at 90, 100, 115, 130 and 145 MeV cm incident energy, and the latter component is not present at the two lowest energies. On the other hand it is very likely that the difference observed (fig. 2) between the ER cross section (720 mb) at 150 MeV (cm) and the expected value of the fusion cross section (’ 1100 mb, see below) is due to compound-nucleus fission. The “fission-like” [6] cross section at 130 MeV was found to be 320 mb. Predictions for the 4oCa t4uCa fusion cross section were given by Glas and Mosel [3], who have used the concepts of critical radius and critical potential. In that framework, the fusion cross section is expected to depend linearly on the quantity E-l, with different slope in the energy ranges below and above the critical energy E,: ~=nRi(l-vn/E)
when EGE,,
u = nR,2( 1 - VJE)
when E>E,,
where R, and R, are the barrier and critical radii, respectively, and VB and V, the corresponding values of the ion-ion potential. On fig. 2, the ER cross section
Volume
73B. number
2
PHYSICS
0°15
l/E,,,,
oo1i5(k”.‘)
Fig. 2. Evaporation-residue cross section as a function of E&. The predictions of Glas and Mosel [ 3 ] are given by the thin line and the dashed line, for an “average” and a “magic” system, respectively. The dashed-dotted line gives the prediction of ref. [lo] and the long-dashed line gives that of ref. [ 91. The thick full line results from a fit using the Glas and Mosel formula.
is plotted as a function of E-l and it is compared to the best fit of the model of Glas and Mosel, obtained with the following parameters VB = 5 1.5 f 0.5 MeV, R,= 10.2kO.5 fm,roB= 1.49 f 0.07 fm, I’, = 24.0 ?I 0.5MeV,Rc=6.65~0.5fm,r0c=0.97~0.07fm.The fusion barrier VB compares well with the value V, = 52.7 + 0.8 MeV determined from our earlier elastic scattering measurements [2]. It is also interesting to note that Glas and Mosel correctly predict a positive value for the critical potential. This classifies the system definitely among the “heavy” ones (light systems have a negative critical potential). However, the value of the fusion barrier suggested in ref. [3] is too high, and the predictions consequently underestimate the ER cross section. One can also notice good agreement between the value of the reduced critical radius and the one (rot = 1.OO+ 0.07 fm) used since the work by Galin et al. [l]. One then can ask whether the fusion of the 4oCa + 4oCa system gives evidence for the closed-shell structure of the colliding nuclei. The answer is clearly negative. From our analysis of the data in the framework of the Glas and Mosel model, both the critical radius and the barrier radius for the 4oCa +40Ca system do not show any deviation from the values obtained for other (non-magic) systems. A similar conclusion is drawn from a recent analysis [S] of the near-to-barrier
LETTERS
13 February
1978
fusion excitation functions for many different systems, including the 4oCa t 4oCa data. The effective nucleusnucleus potential required to reproduce these data follows the macroscopic systematics of many different systems. Such a conclusion is important for a physical interpretation of the concept of critical radius [3]. From the single-particle spectrum of the two-center shell model, as a function of the center separation, Glas and Mosel observe that energy losses can only occur at level crossings. The location of the lowest one would correspond to the critical radius, and it is expected to depend strongly on the structure of the colliding nuclei. Since the analysis of the 40Ca + 4oCa fusion data does not confirm this hypothesis (see the two variants of the Glas and Mosel predictions in fig. 2) one can suppose that the level crossing concept, based on adiabatic calculations, is not sufficient to deduce the microscopic phenomena which are responsible for dissipative processes in heavy-ion reactions. Perhaps fast collective and single-particle excitations provide the first step in overcoming the shell gap before adiabatic effects (such as level crossings) could play a role. These remarks are also valid in connection with the results of a three-dimensional time-dependent HartreeFock calculation by Bonche et al. [4 1. Even if they reproduce the shape of the excitation function, the fusion barrier is obtained at too high energy. Bonche et al. attribute this discrepancy to two reasons: (i) the force used in the calculation and (ii) the imposed spinisospin degeneracy, (i.e. four particles occupying the same spatial orbit). As a result, only 4p-4h excitations are available, and energy dissipation could consequently be underestimated. It should be noticed that the microscopic calculations (which take into account the shell closure of 4%Za) yield an interaction barrier which is too high as compared with the experimental results. On the contrary, macroscopic estimates [9,10] in which the structure of 4oCa is neglected are much more satisfying. These latter estimates have been reported in fig. 2. To summarize, the measurement of the ER cross sections for the 4oCa + 4oCa system, for energies up to three times the Coulomb barrier, is presented and a very efficient experimental method described. No evidence for a specific behavior of the system associated with the shell closure of 4oCa is found. On the contrary, the data indicate that the excitation processes 137
Volume 73B, number 2
PHYSICS LETTERS
(usually referred to as friction) are sufficiently strong to destroy the specific structure of the colliding nuclei already
in the first stages of the collision.
We would like to thank Prof. D.H.E. Gross for several stimulating of this results
discussions
and for communication
prior to publication.
References [l] J. Galin, D. Guerreau, M. Lefort and X. Tarrago, Phys. Rev. C9 (1974) 1081.
138
13 February 1978
[2] H. Doubre et al., Phys. Rev. Cl5 (1977) 693. [3] D. Glas and U. Mosel, Nucl. Phys. A237 (1975) 429. [4] P. Bonche, B. Grammaticos and S.E. Koonin, submitted to Phys. Rev. C. [S] M. Richter et al., Nucl. Phys. A278 (1977) 163. [6] J.C. Roynette et al., Phys. Lett. 67B (1977) 395, and to be published. [ 71 F. Plasil and M. Blann, Phys. Rev. Cl 1 (1975) 508. [8] K. Siwek-Wilczyfiska and J. Wilczyliski, to be published. [9] D.H.E. Gross and H. Kalinowski, private communication. [lo] K. Siwek-Wilczytiska and J. WilczyAski, Nucl. Phys. A264 (1976) 115.