nuclear physics of physics university of ctg.pptx

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1. PRESENTED BY: Israt Sultana Eithu (19201024) Md. Mahiuddin Zilani (20201110) Mohammad Minhaz (20201074) Md Mobarak Hossen (20201068) Seikh Sadia Siddiqua (20201052) Connecting Kurie Plots, Selection Rules, and Range-Energy Relationship Exploring Quantum Phenomena:

2. Outline Introduction Kurie Plot Kurie Plot Analysis Selection Rules Selection Rules in Action Range-Energy Relationship Range-Energy Analysis

3. Introduction Beta decay is a fundamental nuclear process wherein a neutron transforms into a proton, accompanied by the emission of a beta particle (electron or positron) and an antineutrino or neutrino. Understanding the nuances of this decay process is crucial in the study of nuclear physics . Beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Figure-01: β − decay in an atomic nucleus

4. Kurie Plot The K urie plot in the context of beta decay is a graphical representation that helps illustrate the energy spectrum of beta particles emitted during radioactive decay. In beta decay, a radioactive nucleus undergoes a transformation, emitting a beta particle (either an electron, , in beta-minus decay or a positron, Type equation here. , in beta-plus decay) and an antineutrino or neutrino. The Kurie plot typically shows the relationship between the energy of the emitted beta particles and the number of decays at each energy level. the differential energy spectrum is given by,     This gives us the number of β particles/sec in the momentum interval P and P+dP.Now Taken Into account coulomb interaction the spectrum is written in the following form,

5. Kurie Plot Analysis Here, F(Z,P) includes the constants and the dependence of nuclear charge Z for the daughter nucleus. Now the plot of the radical against energy should be a straight line whose intercept with the horizontal axis can be reliably determined. Figure-2: Kurie plot  

6. Kurie Plot Analysis If m ν =0, Fermi- Kurie plot is a straight line and intersects the energy E axis at E β = E given by Eq.1 If m ν ≠0, this plot becomes curved at the maximum end of the energy and intersects the E axis vertically at E=E − m ν c 2 . A determination of the distance between the intersections of extrapolated Fermi- Kurie plot for m ν = 0 and experimental curve on the energy E axis furnishes a value for the mass of the neutrino. Figure 2 shows a Kurie plot for m ν ≠0, which departs from a straight line. One can set an upper limit on neutrino’s mass. Figure-3:Kurie plot showing kink (dotted portion of curve) for mν ≠0 .

7. Selection Rules Besides energy and linear momentum conservation, a nuclear transition must also satisfy angular momentum and parity conservation. The and the ν in the final states of a β decay each have intrinsic spin - . Conservation of total angular momentum requires that :     where, are the total angular momenta of the parent and daughter, respectively, and are the total orbital and total spin angular momentum, respectively, of the ν pair. Therefore, the ∆I can be ±L. or ±|L ± 1|. If L = 0, then ∆I = ±1. There are only two cases for lepton spin alignment. S = 0, when the ν intrinsic spins anti-align, is called a Fermi transition. S = 1, when the ν intrinsic spins align, is called a Gamow-Teller transition.  

8. Selection Rules The entire characterization scheme is given in table below: Table-01: Classification of transitions in β decay. Notes: (∗ ) 0+ → 0 + can only occur via Fermi decay. (∗∗) Unique transitions are Gamow-Teller transitions where are aligned. The shape factors have very simple forms in this case. (∗∗∗) For the n ≥ 2 forbidden transitions, the ∆I = ±(n − 1) transition is often associated with the n − 2 forbidden transition, being indistinguishable in the measurements of these processes.  

9. Range-Energy Relation Although the β rays have a continuous energy spectrum, it is still possible to find a relation between E max , the maximum energy of the spectrum and the corresponding range R. A relation frequently used for a rapid determination of E(MeV) in aluminum is due to Feather R (g cm −2 ) = 0.542E − 0.133 for 0.8 <E< 3 MeV 0.407E 1.38 for 0.15 <E< 0.8 MeV Also, the intensity of β particles from the β decay is found to decrease exponentially with absorption thickness d I = I exp(− μd ); where μ (cm 2 /g) is the absorption coefficient.

10. Real World Example In experiments like the tritium beta decay experiments (KATRIN experiment, for instance), researchers use Kurie plots to analyze the shape of the electron energy spectrum near the endpoint, providing valuable information about the neutrino mass. Kurie plots In the context of beta decay, the conservation of angular momentum and parity are selection rules. Knowledge of these rules helps in predicting the spins and parities of the involved nuclear states, which is crucial for understanding the decay process. Selection rules In experiments studying beta decay, the precise measurement of energy spectra allows researchers to test theoretical models and extract information about fundamental particles, such as neutrino masses and mixing angles. Range-Energy Relation