NERS 312 Elements of Nuclear Engineering and Radiological Sciences II aka Nuclear Physics for Nuclear Engineers Lecture Notes for Chapter 14: α decay Supplement to (Krane II: Chapter 8) The lecture number corresponds directly to the chapter number in the online book. The section numbers, and equation numbers correspond directly to those in the online book. c Alex F Bielajew 2012, Nuclear Engineering and Radiological Sciences, The University of Michigan (cid:13) How α decay works Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 2:14.0 Chapter 14: In this Chapter you will learn ...... Chapter 14.1: Why α Decay Occurs Chapter 14:2 Basic α Decay Processes The energetics of α decay • Relativistic effects? • Chapter 14.3: α-decay systematics As Q increases, t decreases 1/2 • Prediction of Q from the semiempirical mass formula • Chapter 14.4: Theory of α Emission The simplest theory of α emission • Gamow’s theory of α decay • Krane’s treatment of α decay • Comparison with Measurements • Cluster decay probabilities • Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 3:14.0 Chapter 14.5: Angular momentum and parity in α decay Angular momentum • Conservation of angular momentum and parity • Angular intensity of α decays for elliptic nuclei • Chapter 14.5: α-decay spectroscopy Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 4:14.1 14.1—Why α decay occurs The mass excess (in MeV) of 4He and its near neighbors, is shown below. N Z 0 1 2 3 ⇓ \ ⇒ 0 - 7.2889705(1) - - 1 8.0713171(5) 13.1357216(3) 14.9312148(24) 25.32(21) 2 - 14.9498060(23) 2.4249156(1) 11.680(50) 3 - 25.90(10) 11.390(50) 14.086793(15) Thus, we see that, compared to its low-A neighbors in the periodic table, it is bound very strongly. We know, from the shell model of the nucleus, that 4He is a doubly-magic nucleus, and this is what we may have expected. So, thinking classically, occasionally 2 protons and 2 neutrons appear together at the edge of a nucleus, with outward pointing momentum, and bang against the Coulomb barrier. Every once in a while, it can tunnel through, as we saw in 311. Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 5:14.1 Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 6:14.1 So compelling is this concept, that the α particles can stay intact in the nucleus, prompted two-time Nobel Laureate, Linus Pauling (the only person two have won two Nobel Prizes, awarded to a single person): http://en.wikipedia.org/wiki/Linus_Pauling to invent a “spheron model” of the nucleus. Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 7:14.1 Quoting from the SOAK-TN (Source Of All Knowledge, True or Not) On September 16, 1952, Pauling opened a new research notebook with the words ”I have decided to at- tack the problem of the structure of nuclei.”[86] On October 15, 1965, Pauling published his Close-Packed Spheron Model of the atomic nucleus in two well respected journals, Science and the Proceedings of the National Academy of Sciences.For nearly three decades, until his death in 1994, Pauling published numerous papers on his spheron cluster model. The basic idea behind Pauling’s spheron model is that a nucleus can be viewed as a set of “clusters of nucleons”. The basic nucleon clusters include the deuteron [np], helion [pnp], and triton [npn]. Even-even nuclei are described as being composed of clusters of alpha particles, as has often been done for light nuclei. Pauling attempted to derive the shell structure of nuclei from pure geometrical considerations related to Platonic solids rather than starting from an independent particle model as in the usual shell model. In an interview given in 1990 Pauling commented on his model: “Now recently, I have been trying to determine detailed structures of atomic nuclei by analyzing the ground state and excited state vibrational bends, as observed experimentally. From reading the physics literature, Physical Review Letters and other journals, I know that many physicists are interested in atomic nuclei, but none of them, so far as I have been able to discover, has been attacking the problem in the same way that I attack it. So I just move along at my own speed, making calculations...” Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 8:14.1 Who is this person? http://en.wikipedia.org/wiki/Lenny_Susskind Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 9:14.2 14.2—Basic α-decay processes An α decay is a nuclear transformation in which a nucleus reduces its energy by emitting an α-particle. A A 4 4 X X + He , Z N Z−2 N′ 2 2 2 −→ − − or, more compactly : A X X + α . ′ −→ The resultant nucleus, X is usually left in an excited state, followed, possibly, by another ′ α decay, or by any other form of radiation, eventually returning the system to the ground state. Nuclear Engineering and Radiological Sciences NERS 312: Lecture 14, Slide # 10:14.2