By J.M. Arias, M. Lozano
The sphere of nuclear physics is coming into the twenty first century whereas experiencing a robust revival. at the one hand it's altering qualitatively via new experimental advancements that permit us to direct radioactive and different unique probes to focus on nuclei and touch off tremendous full of life nuclear collisions. additionally, the outstanding sophistication of recent detector structures leads us to count on a few new discoveries within the close to destiny. nevertheless many new purposes have seemed in fields as different as drugs, undefined, artwork, archaeology and the environmental sciences. This e-book is an instructional advent to the sphere of recent nuclear physics. it may bridge the space among general textbook fabric and learn literature if you happen to intend to paintings in any of the disciplines the place nuclear technological know-how and know-how goes to play a huge function sooner or later.
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Extra resources for An Advanced Course in Modern Nuclear Physics
4). However, we should have in mind that this expansion is an asymptotic (divergent) series in 1/N . Therefore, corrections of high orders increase, beginning with some number k, which depends on N . Usually, it occurs for sufficiently large values of k. 1/N Expansion for a Particle in Central Potential Well In order to investigate binding states of a particle in the smooth central potential well U (r ) = U0 v(r/R) we choose the expansion parameter N ≡ n = l + nr + 1. 5) In the case of Coulomb potential the quantity n is the principal quantum number.
Imaginary part of the energy E nnr determines the width of such resonance states. Finally, let us underline that the general peculiarities of application of 1/n−expansion for Hulthén potential are correct also for other smooth shortrange potentials (Yukawa potential, exponential potential of the form U (r ) = −U0 exp(−r/R) and so on). 4 Obtain 1/n-expansion for a particle in the short-range central potential U (r ) = U0 v(r/R) for critical value ξnnr ,cr of the parameter ξ≡ m R 2 U0 2 which corresponds to appearing of the level with quantum numbers n, l.
19) the total number of levels in the considered 1. 2: These results allow to make a conclusion that 1/N expansion with terms up to the second order in 1/N is applicable even at N ≥ 1. Bad accuracy occurs for shallow levels only. (b) In this case we obtain E n (1/N ) = n + 1 2 8U0 + 1 + ... 8 The exact expression for energy levels is E nexact = 8U0 n + 1 1 + 2 4 8U0 + 1 − 8U0 . 026. (c) The first three terms of 1/N-expansion give the exact value of the energy spectrum (see , Sect. 23): 1 1 1 U0 b 2 n + E n (1/N ) = E nexact = − U0 b2 + 4 2 2 2 1 =− 2U0 b − (2n + 1) .
An Advanced Course in Modern Nuclear Physics by J.M. Arias, M. Lozano