¾ Spin of many nucleons add to give I. When they pair their spins either: cancel (spins pair antiparallel) pairing of a spin-up and spin-down nucleon add (spins pair parallel) pairing of two nucleons with both spin up or both spin down The valley has the following shape. Spin orbit interaction 5.3.4 . valence nucleons outside filled shells, the Shell Model calculations agree very well with measured values of spin and parity assignments and transition probabilities. An example of transitions between a nucleus’s energy levels is shown in Fig. Pairing of electrons near the Fermi surface with antiparallel momentum and spin (k up; -k down) • Nuclear physics: Pairing of nucleons to total I Z=0 : (m i , -m ) Experimental observations: Odd-even effect in nuclear physics The nuclear mass for given odd A:-> Binding energy for odd nuclei: Energy gap in nuclear physics for low excitations: 5.1 Characteristics of the nuclear force . which may affect the nuclear force. For even number of protons plus even number of neutrons: I0= . levels are ﬁlled the nucleons of each type pair oﬀ, yielding a zero angular momentum for the pair. Both states have the same energy in the SU(4) limit. 12C, 16O 2. The isospin and spin quantum numbers of the nucleon have two states each, resulting in four combinations in total. Paired spins → I = 0. This is a consequence of the spin pairings of nucleons, leading to a limited total nuclear angular momentum. In this part of the course we want to study the structure of nuclei. ¾ Pairing dictated by a shell model of nucleus. the spin-spin or spin-orbit interactions will be different for two states. This pairing of nucleons implies the existence of a pairing force that lowers the energy of the system when the nucleons are paired-oﬀ. The ground states of 12B (5 protons, 7 neutrons) and 12N (7 protons, 5 neutrons) are The microscopic calculation of the spin distribution of level densities in the presence of correlations is a difficult problem. As nucleons are added in a nucleus in a specific state the nucleons get paired and the final spin state of the nucleus is decided by the odd nucleon (its spin). Stable nuclei are found in a narrow band, in the N-Z diagram which is called the valley of stability. IV. My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, proton with neutron. This fact is the most strik ing evidence that the residual interaction plays an important role and leads to pairing of nucleons of the same type within an atomic nucleus. However, spin-triplet pairing becomes fa-vored in nuclei with equal numbers of neutrons N and protons Z when the nucleon number is very large (proba- 6-3. Spin pairing and valence nucleons . Although the spin-triplet interaction is stronger, the spin-orbit ﬁeld tends to suppress pairing in the triplet channel [1,2]. Nucleons Hamiltonian 5.3.3 . (analogous -not identical- to electron spin pairing) ¾ Protons and neutrons add separately. The rules developed for building a nucleus in the nuclear shell model therefore bear a lot of resemblance to Hund's rules for filling electron shells, although the pairing interaction is stronger among nucleons (for which there are two species) than among electrons. Nuclear angular momentum includes not only nucleon spin but also nucleon orbital angular momentum. the scattering cross sections for two states will give different results. between identical nucleons in the spin-singlet channel. Most nuclei and their isotopes are unstable. This will be shown explicitly the example presented in Sec. ¾ Spins pair up. Since the nucleons get paired-oﬀ, the total spin and Some basic rules: 1. 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