Key Topics in Nuclear Structure - Proceedings of the 8th International Spring Seminar on Nuclear Physics, 2005
Motivated by the problem of the relative importance of J = 1+ T = 0 pairing versus the better est... more Motivated by the problem of the relative importance of J = 1+ T = 0 pairing versus the better established J = 0+ T = 1 pairing in nuclei, we here address the problem of the number of np pairs of a given angular momentum in selected nuclei, 44Ti, 46Ti, and 48Ti. The number of pairs is obviously relevant to np pickup reactions such as (p,3He). One can address also the np transfer reaction (3He,p) and indeed there is a proposal by the Berkeley group to do the reaction 44Ti(3He,p)46Sc. In this work we will consider the single j shell model for the Ti isotopes. In the near future more elaborate calculations are planned.
We discuss different nuclear structure properties that may lead to spin suppression in magnetic d... more We discuss different nuclear structure properties that may lead to spin suppression in magnetic dipole excitations (as well as in Gamow-Teller transitions). We especially compare the triaxial and the axial asymptotic deformation limits and show that the summed B(M1) strength can be quite different in the two cases. A connection between triaxial deformation and spin suppression is established. It is kriown, however, that modern Hartree-Fock calculations yield axially symmetric solutions for several nuclei which were previously thought to be triaxial. We show that taking into account the effects of higher shells can lead to an enhanced orbital contribution to M1 excitations without affecting ground-state magnetic moments.
... and Reactions," International School of Physics, Enrico Fermi, Course XXXVI, p. 247, (C.... more ... and Reactions," International School of Physics, Enrico Fermi, Course XXXVI, p. 247, (C. Block, Ed.), Academic Press, New York, 1966. 15. DM BRINK AND E. BOEKER, Nuel. Phys. A 91 (1967), 1. 16. E. MOYA DE GUERRA, P. SARRIGUREN, JA CABALLERO, M. CASAS, AND ...
Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum... more Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei $$S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2<r^2>^2) \mu^2_N$$ with B(E2) the E2 strength for the transition from the ground state to the first excited state in
We discuss different nuclear structure properties that may lead to spin suppression in magnetic d... more We discuss different nuclear structure properties that may lead to spin suppression in magnetic dipole excitations (as well as in Gamow-Teller transitions). We especially compare the triaxial and the axial asymptotic deformation limits and show that the summed /ital B/(/ital M/1) strength can be quite different in the two cases. A connection between triaxial deformation and spin suppression is established.
We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properti... more We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances ∆(1230) and ∆(1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.
... Rev. 128, 812 (1962); W. Bertozzi, Nucl. Phys. A374, 109c (1982); B. Frois, in Proceed-ings o... more ... Rev. 128, 812 (1962); W. Bertozzi, Nucl. Phys. A374, 109c (1982); B. Frois, in Proceed-ings of the International Conference on Nuclear Physics, Florence, 1983, edited by P. Blasi and RA Ricci (Tipografia Compositori, Bologna, 1984), p. 221; A. Richter, ibid., p. 189. 4E. ...
In these talks, we review non relativistic selfconsistent mean field theories, their scope and li... more In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime, ..., to detailed structure in excitation spectra (high spin, RPA modes, ...), as well as charge, magnetization and velocity distributions.
ABSTRACT ATDHF formulations for large amplitude collective nuclear modes are reviewed together wi... more ABSTRACT ATDHF formulations for large amplitude collective nuclear modes are reviewed together with the conditions of validity that establish the range of applicability of the theory. Application to soluble models is presented to clarify the meaning of different validity conditions and equations of path. Extensions of the standard ATDHF formalism are also discussed.
Key Topics in Nuclear Structure - Proceedings of the 8th International Spring Seminar on Nuclear Physics, 2005
Motivated by the problem of the relative importance of J = 1+ T = 0 pairing versus the better est... more Motivated by the problem of the relative importance of J = 1+ T = 0 pairing versus the better established J = 0+ T = 1 pairing in nuclei, we here address the problem of the number of np pairs of a given angular momentum in selected nuclei, 44Ti, 46Ti, and 48Ti. The number of pairs is obviously relevant to np pickup reactions such as (p,3He). One can address also the np transfer reaction (3He,p) and indeed there is a proposal by the Berkeley group to do the reaction 44Ti(3He,p)46Sc. In this work we will consider the single j shell model for the Ti isotopes. In the near future more elaborate calculations are planned.
We discuss different nuclear structure properties that may lead to spin suppression in magnetic d... more We discuss different nuclear structure properties that may lead to spin suppression in magnetic dipole excitations (as well as in Gamow-Teller transitions). We especially compare the triaxial and the axial asymptotic deformation limits and show that the summed B(M1) strength can be quite different in the two cases. A connection between triaxial deformation and spin suppression is established. It is kriown, however, that modern Hartree-Fock calculations yield axially symmetric solutions for several nuclei which were previously thought to be triaxial. We show that taking into account the effects of higher shells can lead to an enhanced orbital contribution to M1 excitations without affecting ground-state magnetic moments.
... and Reactions," International School of Physics, Enrico Fermi, Course XXXVI, p. 247, (C.... more ... and Reactions," International School of Physics, Enrico Fermi, Course XXXVI, p. 247, (C. Block, Ed.), Academic Press, New York, 1966. 15. DM BRINK AND E. BOEKER, Nuel. Phys. A 91 (1967), 1. 16. E. MOYA DE GUERRA, P. SARRIGUREN, JA CABALLERO, M. CASAS, AND ...
Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum... more Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei $$S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2<r^2>^2) \mu^2_N$$ with B(E2) the E2 strength for the transition from the ground state to the first excited state in
We discuss different nuclear structure properties that may lead to spin suppression in magnetic d... more We discuss different nuclear structure properties that may lead to spin suppression in magnetic dipole excitations (as well as in Gamow-Teller transitions). We especially compare the triaxial and the axial asymptotic deformation limits and show that the summed /ital B/(/ital M/1) strength can be quite different in the two cases. A connection between triaxial deformation and spin suppression is established.
We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properti... more We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances ∆(1230) and ∆(1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.
... Rev. 128, 812 (1962); W. Bertozzi, Nucl. Phys. A374, 109c (1982); B. Frois, in Proceed-ings o... more ... Rev. 128, 812 (1962); W. Bertozzi, Nucl. Phys. A374, 109c (1982); B. Frois, in Proceed-ings of the International Conference on Nuclear Physics, Florence, 1983, edited by P. Blasi and RA Ricci (Tipografia Compositori, Bologna, 1984), p. 221; A. Richter, ibid., p. 189. 4E. ...
In these talks, we review non relativistic selfconsistent mean field theories, their scope and li... more In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime, ..., to detailed structure in excitation spectra (high spin, RPA modes, ...), as well as charge, magnetization and velocity distributions.
ABSTRACT ATDHF formulations for large amplitude collective nuclear modes are reviewed together wi... more ABSTRACT ATDHF formulations for large amplitude collective nuclear modes are reviewed together with the conditions of validity that establish the range of applicability of the theory. Application to soluble models is presented to clarify the meaning of different validity conditions and equations of path. Extensions of the standard ATDHF formalism are also discussed.
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