{Lambda} single particle energies

Journal Article · Mon Nov 01 04:00:00 EST 1999 · Physical Review, C

DOI:https://doi.org/10.1103/PhysRevC.60.055215· OSTI ID:692563

Usmani, Q N ^[1]; Bodmer, A R ^[2]

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1. Department of Physics, Faculty of Science and Environmental Studies, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor (Malaysia)
2. Physics Division, Argonne National Laboratory, Argonne, Illinois 60439-4843 (United States)

The {Lambda} single-particle energies B{sub {Lambda}} of hypernuclei (HN) are calculated microscopically using the Fermi hypernetted chain method to obtain for our {Lambda}N and {Lambda}NN potentials the {Lambda} binding D({rho}) to nuclear matter, and the effective mass m{sub {Lambda}}{sup {asterisk}}({rho}) at densities {rho}{le}{rho}{sub 0} ({rho}{sub 0} is normal nuclear density), and also the corresponding effective {Lambda}N and {Lambda}NN potentials. The {Lambda} core-nucleus potential U{sub {Lambda}}(r) is obtained by suitably folding these into the core density. The Schr{umlt o}dinger equation for U{sub {Lambda}} and m{sub {Lambda}}{sup {asterisk}} is solved for B{sub {Lambda}}. The fringing field (FF) due to the finite range of the effective potentials is theoretically required. We use a dispersive {Lambda}NN potential but also include a phenomenological {rho} dependence allowing for less repulsion for {rho}{lt}{rho}{sub 0}, i.e., in the surface. The best fits to the data with a FF give a large {rho} dependence, equivalent to an {ital A} dependent strength consistent with variational calculations of {sub {Lambda}}{sup 5}He, indicating an effective {Lambda}NN dispersive potential increasingly repulsive with {ital A} whose likely interpretation is in terms of dispersive plus two-pion-exchange {Lambda}NN potentials. The well depth is 29{plus_minus}1&hthinsp;MeV. The {Lambda}N space-exchange fraction corresponds to m{sub {Lambda}}{sup {asterisk}}({rho}){approx}0.75{endash}0.80 and a ratio of {ital p}- to {ital s}-state potentials of {approx}0.5{plus_minus}0.1. Charge symmetry breaking (CSB) is significant for heavy HN with a large neutron excess; with a FF the strength agrees with that obtained from the A=4&hthinsp;HN. The fits without FF are excellent but inconsistent with the requirement for a FF, with {sub {Lambda}}{sup 5}He, and also with the CSB sign for A=4. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 692563
• Journal Information: Physical Review, C, Journal Name: Physical Review, C Journal Issue: 5 Vol. 60; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ATOMIC NUMBER
BARYON-BARYON INTERACTIONS
HYPERNUCLEI
LAMBDA BARYONS
NUCLEAR FORCES
NUCLEAR MATTER
NUCLEON-NUCLEON POTENTIAL
SCHROEDINGER EQUATION
SINGLE-PARTICLE MODES
SYMMETRY BREAKING