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The Effect Of Gamma Softness on the 2+ Energy in 190 W

The Effect Of Gamma Softness on the 2+ Energy in 190 W. Emma Suckling. Supervisors: Dr. M Oi & Dr. P D Stevenson. Overview. Significance of 190 W Why study it? Experimental data Rotational band structure Gamma softness Theoretical calculation

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The Effect Of Gamma Softness on the 2+ Energy in 190 W

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  1. The Effect Of Gamma Softness on the 2+ Energy in190W Emma Suckling Supervisors: Dr. M Oi & Dr. P D Stevenson

  2. Overview • Significance of 190W • Why study it? • Experimental data • Rotational band structure • Gamma softness • Theoretical calculation • Production of single-particle states in 190W • Construction of Slater determinants as an approximation to the full many-body state • Generator coordinate method to incorporate gamma softness and angular momentum projection of 2+ state • Progress • Conclusion & future work

  3. 190W - Most neutron-rich isotope of W - Several protons and neutrons away from the magic numbers

  4. Experimental Data Zs. Podolyák et. al., Phys. Lett. B 491 (2000) 225-231 - Established rotational band structure - Inferred gamma softness - 4+/2+ shows deviation from pattern in lighter isotonic chains

  5. Theoretical Calculation • Production of single-particle states in 190W • Nilsson model • Construction of many-body trial wavefunction as an approximation to the collective state • Slater determinants • Incorporate gamma softness into the model • Generator coordinate method • Restore broken rotational symmetry • Angular momentum projection

  6. Production of S.P States • Diagonalise deformed Nilsson Hamiltonian • h0 is spherical harmonic oscillator • Spin orbit and l2 term included • Deformed Nilsson states expanded in terms of spherical Nilsson basis (nljm) • Resulting single-particle energies plotted as a function of deformation in Nilsson diagrams

  7. Many Body States • Construct a set of Slater determinants from single-particle states as trial wavefunctions • ak+ are fermion creation operators corresponding to deformed Nilsson states • We can relate deformed and spherical fermion operators by the expansion coefficients of φk

  8. Generator Coordinate Method • Apply GCM to incorporate gamma softness • Solve the Hill-Wheeler equation to obtain f() • Minimise the expectation of the many-body Hamiltonian with respect to f() • Angular momentum projection is a special case of GCM and restores broken rotational symmetry • In this case f() has an analytic form which allows the projected energy to be calculated

  9. Progress

  10. Future Work • Continue code development to include generator coordinate method and angular momentum projection • Calculate 2+ and 4+ energies in 190W and surrounding nuclei • Study of high spin nuclei including wobbling incorporating similar projection techniques

  11. Thank You • Makito & Paul • For listening!

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