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Alternatively, one may combine Chiste's method with a random search procedure. 2 Modified Newton-Sabatier inversion method The modified Newton-Sabatier scheme has been introduced by Miinchov and Scheid [2] using the physical assumption that most interactions of quantum physics are known beyond a certain radial distance TO. For example, this interaction is the repulsive Coulomb potential in the heavy ion collisions. Also they showed that the proofs of existence and uniqueness of the solutions of the method hold if an infinite number of phase shifts are involved in the procedure.

The unknown reduced transition probability B(E2: 0+ to 2+) of 68Ni should then be measured in order to confirm this shell effect. In this respect, it would be interesting to compare this B(E2) value to that of the doubly magic 56Ni, which was found to be 600 (120) e2 fm 4 [1]. For heavier N=40 isotones, proton excitations in the fp-shell increase the collectivity to B(E2)=1600(140) e2fm 4 for 70Zn [11] and 2130(60) e2fm 4 for 72Ge [11]. Another feature of the N =40 nuclei is that they exhibit a 0+ 2 state at relatively low excitation energy.

3 MeV) of the four segmented clover detecors, the increase of the secondary beam intensities allowed an unambiguous determination of the B(E2: 0+ to 2+) value in 66Ni and 68Ni. The obtained values have been added to the systematics in figure 3. This indicates for the first time the effectiveness of the N=40 spherical shell effect in the Ni isotopes. 1200 4000 \ 1000 800 600 400 . 5 N .. lo: ~ 24 28 32 36 40 44 1800 Zn * +' [;;;l 0 24 28 32 36 40 44 / N 750 Ge Ii::! 1300 == 500 24 28 32 36 40 44 800 24 28 32 36 40 44 3000 1100 2500 2000 Ni 600 1500 1000 24 28 32 36 N 40 44 100 24 28 32 36 40 44 N Figure 3 Systematics of the 2+ energies and B(E2) values in the Ge,Zn and Ni isotopes.

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An Introduction to the Theory of Optics (2007)(en)(356s) by Schuster A.

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