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PHYSICAL REVIEW C VOLUME 63 034608 Rare isotope production in statistical multifragmentation Scott Pratt Wolfgang Bauer Christopher Morling and Patrick Underhill Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory Michigan State University East Lansing Michigan 48824 Received 22 September 2000 published 14 February 2001 Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble Both the initial fragmentation and the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments The importance of sequential decay exact particle number conservation and the sensitivities to parameters such as density and temperature are explored Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture DOI 10 1103 PhysRevC 63 034608 PACS number s 25 70 Pq 24 10 Pa 64 60 My I INTRODUCTION The study of rare isotopes is attracting increasing attention due to the recent development of radioactive beam facilities where isotopes are produced through nuclear collisions Projectile and target nuclei might vary in size from a few dozen nucleons all the way to uranium The mechanism for rare isotope production might entail the transfer of a few nucleons between the projectile and target induced fission of the projectile or at highest energy transfer multifragmentation This last mechanism which assumes temperatures of a few MeV is the focus of this study Multifragmentation is an extremely complicated process that takes place at a time scale of 100 fm c At such excitations tunneling through barriers plays a less central role than in fission In this short time the system is able to sample an enormous number of configurations which makes dynamical calculations computationally very intensive However this very complexity lends justification to statistical calculations which have proven remarkably successful in predicting mass yields for excitation energies in the range of a few MeV per nucleon 1 2 It is our aim to apply simple statistical calculations to the study of the production of rare isotopes nuclei with neutronto proton ratios far from the valley of stability Our investigation addresses a variety of questions 1 How do yields depend on the physical parameters of the thermalized system Such parameters are size overall neutron excess density and temperature 2 How sensitive are the yields with respect to various aspects of the modeling such as breakup density level densities and barrier penetration probabilities 3 Is there a qualitative and possibly quantitative explanation for the isospin amplification effects seen for light isotopes Furthermore do these effects carry over into the production of heavier or exotic isotopes It has been experimentally observed that the ratio of mirror nuclei e g 15 O 15N or t 3 He can be of order 10 even though the Current address Department of Physics Washington University Campus Box 1105 One Brookings Drive St Louis MO 63130 0556 2813 2001 63 3 034608 10 15 00 neutron to proton ratio of the colliding nuclei is less than 1 5 3 4 By dividing the ratio of isotope yields from the fragmentation of 124Sn by the same ratio from the fragmentation of 112Sn one can extract the relative chemical potentials between the two systems which appears to be robust with respect to sequential decay Can these results be quantitatively understood within the framework of a statistical model 5 Might multifragmentation provide a superior environment for the production of exotic isotopes in certain regions of the N Z plane Currently abrasion ablation models 4 6 provide the preferred scenario for creating rare isotopes and experiments have focused on searching for rare fragments at projectile rapidities The EPAX parametrization 7 which is in common use for designing experiments is built around such a picture It is not clear to what degree multifragmentative pictures can either complement or compete with abrasion ablation models The canonical ensemble is employed in this study The motivation for choosing the canonical ensemble along with descriptions of the statistical fragmentation algorithm and the sequential decay calculation appear in the next section Isotope yields are primarily determined by the breakup temperature and sequential decay These themes are introduced in Sec III The importance of enforcing exact conservation of overall charge and baryon number with the canonical ensemble is discussed in Sec IV The sensitivity to the size and neutron excess of the overall system is explored in Sec V while Sec VI contains a study of the sensitivities to several aspects of the model such as breakup density level density and tunneling through the Coulomb barrier during the sequential decay process Recently Xu et al have measured yields of light fragments from the fragmentation of both 112 Sn and 124Sn and by taking ratios of isotope yields have determined the relative chemical potentials of the two systems 3 This result is interpreted in Sec VII A summary is provided in Sec VIII II MODELING STATISTICAL MULTIFRAGMENTATION AND THE SUBSEQUENT DECAY The initial statistical fragmentation of the system is calculated assuming the canonical ensemble The choice of the 63 034608 1 2001 The American Physical Society PRATT BAUER MORLING AND UNDERHILL PHYSICAL REVIEW C 63 034608 canonical ensemble is explained in the following subsection The recursive method described in Sec II B provides a probability for creating any state of any nuclide The modeling of the subsequent sequential decay is described in Sec II C A Choosing a statistical ensemble for fragmentation calculations Statistical calculations have proven remarkably successful in describing mass yields for multifragmentative processes Such models assume a fixed volume where all distributions of N neutrons and Z protons into various fragments and excited states are considered A rather wide variety of thermal models have been employed in the study of nuclear fragmentation including grand canonical 8 canonical 1 and microcanonical 2 treatments Additionally isospin effects have been studied in lattice gas models 9 11 and in percolation 12 13 Since our goal is to study the yields of rarely produced isotopes which may be produced in future radioactive beam facilities as rarely as in one per 1017 events we employ the methods