A study of deformation in light nuclei: (I). Application to the ground state band of 20Ne and to the low-energy spectrum of 19F

Abstract The properties of the ground state band of 20Ne are shown to be well described by the set of wave functions projected from a single intrinsic state. Particular deformed states of nuclei around 16O may be constructed by breaking up the 16O core in such a manner as to produce two protons and two neutrons in the (2s, 1d) shell. Following an observation by Christy and Fowler, the wave function for these four particles is described in terms of the ground state 20Ne band and deformed states are obtained by coupling 1p hole states on to the members of this band. The odd-parity levels of 19F are described by coupling p 1 2 and p 3 2 proton holes on to the ground state 20Ne band and it is shown that the measured E1 transitions in 19F provide evidence for states of this structure. It is also shown that the low-lying even-parity levels of 19F are well described in terms of a single K = 1 2 + band , and these states are compared directly with those obtained from a full intermediate coupling calculation. Overlaps of over 99% are obtained for the ground state ( 1 2 + ) and the 5 2 + members of the band. The structure of the K = 1 2 + band is interpreted on the basis of the nucleus having permanent P4 as well as P2 (Nilsson) type distortions. Electromagnetic transitions in 19F are discussed in detail and the results for the odd-parity states are compared with those of a similar calculation by Harvey in the SU3 scheme. A detailed study of the levels in 19F in the region of 4 to 5 MeV excitation is made and the extent to which core deformation is important in the even parity states is discussed on a semi-quantitative basis. The properties of the 3.91 MeV level (possibly a doublet) are crucial to the detailed interpretation of this nucleus.

[1]  J. Olness,et al.  Gamma-Ray Transitions between the Low-Lying Levels of F 18 , 1967 .

[2]  G. Jones,et al.  LIX. The magnetic moment of the 200 kev excited state of 19F , 1956 .

[3]  H. F. Lutz,et al.  Excitation of the ground state band of 19F by 13.9 MeV proton scattering , 1966 .

[4]  D. Wilkinson,et al.  Beta Decay of O 19 : States of F 19 , 1966 .

[5]  H. Rose,et al.  ANGULAR DISTRIBUTIONS OF GAMMA RAYS IN TERMS OF PHASE-DEFINED REDUCED MATRIX ELEMENTS. , 1967 .

[6]  C. Brihaye,et al.  P4 deformation in an independent-particle model of light nuclei , 1967 .

[7]  D. Clément,et al.  A shell-model calculation of 18F and 18O using the Tabakin interaction , 1968 .

[8]  I. Talmi,et al.  Shell model and deformed states in O18 , 1965 .

[9]  A. Arima,et al.  The structure of the sd-shell nuclei (I). C18, F18, O19, F19 and Ne20 , 1964 .

[10]  R. Ollerhead,et al.  Angular correlation measurements in the O18(p, p′ γ)O18 reaction , 1965 .

[11]  G. Bertsch.  Deformations in perturbation theory , 1966 .

[12]  H. Gove,et al.  Rotational Bands inNe20 , 1961 .

[13]  H. Gove,et al.  LIFETIMES OF THE LOW-LYING LEVELS OF 20NE, , 1965 .

[14]  R. Dreizler,et al.  Hartree-fock method and variation of projected determinants , 1968 .

[15]  E. Warburton,et al.  GAMMA TRANSITIONS IN SELF-CONJUGATE NUCLEI , 1958 .

[16]  A. Arima,et al.  Weak coupling model of particles and holes in the sd shell nuclei , 1967 .

[17]  F. Palumbo.  Intrinsic motion and translational invariance in shell-model calculations , 1967 .

[18]  I. Hamamoto,et al.  Projected wave function from the Nilsson model in 19F , 1968 .

[19]  John Archibald Wheeler,et al.  NUCLEAR CONSTITUTION AND THE INTERPRETATION OF FISSION PHENOMENA , 1953 .

[20]  A. E. Litherland,et al.  E3 Coulomb excitation of F19 , 1963 .

[21]  E. Paul.  The interpretation of the levels of 19F on the rotational model , 1957 .

[22]  K. Yagi,et al.  Experiment on O 18 ( p , γ)F 19 Reaction , 1963 .

[23]  M. Harvey.  Negative parity states in F19 , 1964 .

[24]  L. Zamick.  The importance of the strong isotopic spin dependence of particle-hole matrix elements on the many particle-many hole states in nuclei☆ , 1965 .

[25]  T. Kuo,et al.  Comparison of the Yale, Reid and Hamada-Johnston potentials in shell-model calculations , 1967 .

[26]  R. J. Ord-Smith.  The Symmetry Relations of the 12j Symbol , 1954 .

[27]  T. Engeland,et al.  Core excitation in O18 , 1965 .

[28]  J. Becker,et al.  Electric Quadrupole Transitions near A = 16 : the Lifetimes of the N 16 0.120-, F 18 1.125-, F 19 0.197-, and Ne 19 0.241-MeV Levels , 1967 .

[29]  A. H. Wapstra,et al.  1964 atomic mass table , 1965 .

[30]  M. H. Macfarlane,et al.  A shell-model study of the isotopes of O, F and Ne , 1968 .

[31]  D. Kurath.  Enhancement of E2 transition probability , 1960 .

[32]  E. Warburton,et al.  STUDY OF THE LOW-LYING LEVELS OF F$sup 18$ BY MEANS OF THE O$sup 16$(He$sup 3$, p gamma) F$sup 18$ REACTION , 1965 .

[33]  J. Hope,et al.  Symmetry Properties of the Wigner 9j Symbol , 1954 .

[34]  Frank Tabakin.  An effective interaction for nuclear hartree-fock calculations , 1964 .

[35]  S. Moszkowski,et al.  Nuclear matter calculations using the separation method , 1962 .

[36]  A. de-Shalit.  CORE EXCITATIONS IN NONDEFORMED, ODD-A NUCLEI , 1961 .

[37]  D. Youngblood,et al.  LIFETIME OF THE 1.042-MeV STATE IN $sup 18$F. , 1967 .

[38]  P. Federman.  SHELL-MODEL AND DEFORMED STATES IN OXYGEN ISOTOPES. , 1967 .

[39]  G. Rakavy.  Rotational spectra of nuclei following O16 , 1957 .

[40]  J. Olness,et al.  Studies of F 18 from the O 16 (He 3 ,pγ)F 18 Reaction , 1966 .

[41]  G. Salmon,et al.  The 19F(p,p') reaction at 140 MeV , 1964 .

[42]  G. E. Brown,et al.  Structure of finite nuclei and the free nucleon-nucleon interaction: An application to 18O and 18F , 1966 .

[43]  J. Durell,et al.  Spectroscopic factors for 19F from the 18(3He, d) 19F reaction☆ , 1968 .

[44]  L. Satpathy,et al.  Validity of Hartree-Fock calculations before angular momentum projection - a test in 20Ne , 1968 .

[45]  G. Morpurgo.  Inhibition of M1 ? Transitions with ?T=0 in Self-Conjugate Nuclei , 1958 .

[46]  G. Barton,et al.  Quadrupole enhancement in O17 and F17 , 1959 .

[47]  I. Unna,et al.  USE OF EFFECTIVE INTERACTIONS IN THE ANALYSIS OF DEFORMED NUCLEI , 1963 .

[48]  M. G. Redlich.  INTERACTIONS BETWEEN CONFIGURATIONS OF THREE NUCLEONS IN THE 1d, 2s SHELL , 1955 .

[49]  R. A. Ferrell,et al.  COLLECTIVE ENHANCEMENT OF E2 MATRIX ELEMENTS IN LIGHT NUCLEI , 1959 .

[50]  J. P. Allen,et al.  STUDIES ON $sup 19$F IN THE $sup 18$O(p,$gamma$)$sup 19$F REACTION , 1965 .

[51]  J. Olness,et al.  Levels of F 18 from the O 16 ( He 3 , p γ ) F 18 Reaction , 1967 .

[52]  J. D. Prentice,et al.  The spins and parities of the 1.35 and 1.46 MeV levels of F19 , 1963 .

[53]  R. Bock,et al.  Distorted-wave analysis of the 16O(3He,p)18F reaction at 18 MeV , 1967 .

[54]  R. Ollerhead,et al.  A study of some excited states of 19F by an angular correlation technique , 1966 .

[55]  T. Alexander,et al.  The lifetimes of the 937 and 1082 KeV states of 18F , 1966 .

[56]  B. Giraud,et al.  Projected Hartree-Fock Spectra in Light Nuclei , 1965 .

[57]  E. Warburton.  Spin Assignment for the F18 1.131-MeV Level , 1967 .

[58]  B. Robertson,et al.  Lifetime measurements in 18Ne , 1968 .

[59]  E. F. Bennett.  (p, d) Pickup Reactions in Light Nuclei , 1961 .

[60]  M. G. Redlich.  Interactions between Some Two-Nucleon Configurations , 1954 .

[61]  B. Heusch,et al.  Angular-Correlation Studies of the Reactions O 16 (He 3 ,pγ)F 18 and O 16 (He 3 ,αγ)O 15 , 1967 .

[62]  T. Daniels,et al.  The level structure of 18O and 19O by stripping reactions , 1965 .

[63]  B. H. Flowers,et al.  A study of deformation in light nuclei: (II). Application to the even-parity states of the mass-18 nuclei , 1969 .

[64]  R. Barrett.  THE SCATTERING OF NEUTRONS BY POLARIZED DEFORMED NUCLEI , 1964 .

[65]  A. Kallio,et al.  An application of the separation method in shell-model calculation , 1964 .

[66]  S. Shlomo,et al.  Calculated gamma transitions between 18O levels , 1968 .