Czechoslovak Journal of Physics B

, Volume 29, Issue 7, pp 718–736 | Cite as

Brueckner calculations in harmonic oscillator basis

II. The ground state of the4He nucleus
  • J. Blank


The binding energy (b.e.), r.m.s. radius and charge form factor of the4He nucleus are calculated for the Hamada-Johnston potential using the method developed in part I of this study. The single-particle spectrum is derived from that of a harmonic oscillator by means of an overall shiftC and state-dependent shiftsηh of occupied levels. Theη's are chosen self-consistently and the dependence of results onC and oscillator frequencyΩ is examined. Third-order diagrams in the BG expansion for energy are explicitly calculated (except those belonging to the three-particle cluster) and their importance for getting a weak dependence of the b.e. onC is demonstrated. Dependence onΩ remains rather strong; arguments are given in favour of the choice ofΩ that minimizes second-order diagrams. Effects due to the motion of the centre of mass of the nucleus are eliminated by subtracting 〈TCM〉 calculated up to the second order, the usual zero-order approximation of 〈TCM〉 being shown to overestimate the b.e. by 3–5 MeV. The computed b.e. and r.m.s. radius represent about 50% and 110% of experimental values respectively. The form factorFch(q) was computed for 0≦q2≦20 fm−2; the first-order approximation is a good fit to experimental data, while in the second order diagrams appear that worsen the fit forq2 > >10 fm−2.


Experimental Data Binding Energy Form Factor Harmonic Oscillator Weak Dependence 


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Copyright information

© Academia, Publishing House of the Czechoslovak Academy of Sciences 1979

Authors and Affiliations

  • J. Blank
    • 1
  1. 1.Faculty of Mathematics and Physics, PragueNuclear CentrePraha 8Czechoslovakia

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