Closing a shell-> Stable atom, high ionization energy

Trends in Nuclear Stability See also: T&R Fig Please note two things from this figure: 1.The binding energy per nucleon peaks at 56 Fe (CALM) 2.Note the peaks at 4 He 16 O, and (to some extent) at 12 C.

Shell model for Nuclei From E. Segre “Nuclei and Particles” 3-D Harmonic Oscillator Spherical Square well

Types of Radiation

Types of Radiation Alpha (  ): 4He nucleus; very easy to stop (paper,etc.) Beta (  ) Electrons or positions, relatively easy to stop NOTE: you can also get high-energy electrons through “internal conversion” and the Auger process, but strictly speaking, these do not come from beta decay, and are therefore not, technically, “beta” particles (even though they behave exactly the same way). Gamma (  ) High-energy photons (of nuclear origin) X-rays High-energy photons (of atomic origin) Neutron (n) Protons, ions

Types of Nuclear Decay Alpha (  ): 4He nucleus; Beta (  ) Electrons or positions, of nuclear origin Electron Capture Gamma (  ) (gamma, internal conversion do not change nucleons). Spontaneous fission proton Neutron (n)

Electron Capture An alternative to positron emission (in which a proton converts to a neutron within the nucleus by emitting a positively charged particle) is “electron capture” in which an atomic electron is absorbed by the nucleus (also converting the proton to a neutron). This event will most likely take place when the energy available in the decay is less than that needed to create a positron. What kind of electron would most likely be involved? What signatures might you expect from such an event? Examples: 7 Be, 37 Ar, 41 Ca, 49 V, 51 Cr, 53 Mn, 57 Co, 58 Ni

Beta Radiation Decay

Beta Radiation Decay- Neutrinos The energy of the  particle (electron or positron) is not fixed, this led Pauli to suggest that another unobserved (unobservable?) particle must also be involved in the decay. The “neutrino” was the name given by Fermi a few years later after he developed a theory for the above curve (and after Chadwick discovered the neutron). About 10 of the CALM respondents last night did not quote this as the reason for the energy distribution in beta decay).

Typical Decay scheme Most alpha, beta, EC, n, fission etc. decay (but not all, 210 Po for example) leave the daughter nucleus in an excited state, and a gamma ray is (eventually) produced to take the daughter to its ground state.

Typical Decay scheme II Nuclei can decrease their proton number by one in three ways, positron emission (the most common) Electron capture (much more rarely; see next slide), or proton emission (very rare).

Examples What is the binding energy per nucleon of 56 Fe? The mass of I is u and that of Te is u. What decay mode is possible between these two nuclei?

Cross Sections and Rates The decay rate is proportional to the number of nuclei present, this leads to an exponential time dependence dN/dt=- N(t) implies N(t)=N o exp(- t) The production of active nuclei from stable ones is an example of a generalized scattering experiment (flux times number of target nuclei per unit area, times “area” per nucleus): Rate=nt  Where n-number density, t-thickness,  - cross section (1 barn= cm 2 ),  -flux

Examples A foil of natural In that is 1.0 mm thick is placed in a thermal neutron beam (v=2200 m/s) of flux 10 7 n/cm 2.s. In has a molecular weight of g/mole, and a density of 7.31 g/cm In is a beta emitter and we will assume that it is only produced in a state that decays with a 54 min half life. a). What is the flux of neutrons on the back side of the foil? b). If the foil is in the beam for 1.0 min, what is the activity due to 116 In? c). What is the 116 In activity if the foil is in the beam for 10 hours? The information at the website on the following slide may be useful.

Cross Sections

Alpha Decay T&R Fig

Lecture 23 Potential Barrier: Alpha decay The deeper the “bound” state is below the top of the barrier, the lower will be the kinetic energy of the alpha particle once it gets out, and the slower will be the rate of tunneling (and hence the longer the half-life). Figures from Rohlf “Modern Physics from  to Z o ”.

S-Process