Finding Magic Numbers for Heavy and Superheavy Nuclei. By Roger A. Rydin Associate Professor Emeritus of Nuclear Engineering

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1 Finding Magic Numbers for Heavy and Superheavy Nuclei By Roger A. Rydin Associate Professor Emeritus of Nuclear Engineering

2 Foreword I am a Nuclear Engineer, Specializing in Reactor Physics Nuclear Physics = Physics of Nucleus Theory Taught by Robley Evans, Experiments by Norm Rasmussen Fascinated by Magic Numbers, SemiEmpirical Binding Energy Formula Disturbed by Fast Moving Nucleons in Nucleus, Coulomb Barrier Penetration

3 Foreword Met Dr. Charles Lucas at U. Tulsa Meeting PhD Theoretical Physics W&M, Newport News Accelerator, Expert in Pion/Muon Physics, Now Owns Company Models of Nucleons as Charge Carrying Ring Magnets Nucleus Model in Fixed Static Shells Under Force Balance Explained Magic Numbers New Semi-Empirical BE Formula

4 Foreword Joint Letter to NSE, Published 2009 Sent Copy to Professor Hans Weber He Suggested Application to Superheavy Nuclei Summary T/E by Dr. Mohini Gupta Gupta Suggests Annals of Nuclear Energy Paper Published December 2010 Follow On Paper Published August 2011

5 Order of Presentation Robley Evan s 1950s Nuclear Physics for Engineers Magic Numbers and the Semi-Empirical Binding Energy Formula Lucas Electromagnetic Model of the Nucleus Superheavy Nuclei New Magic Proton and Neutron Numbers Consequences for Selected Isotopes

6 The Atomic Nucleus Heavy on Experimental Data Analysis of What the Data Implied Theory of the Time Not Cut in Stone Orderly Treatment: Charge; Size; Mass; Moments; Isotopes; Nuclear Systematics; Forces; Nuclear Models

7 Nuclear Magic Numbers 2, 8, 28, 50, 82, 126 Are Closed Shells of Some Kind -> Extra Stable Isotopes Helium-4 (2p, 2n) = Alpha Decay Oxygen-16 (8p, 8n) -> UO2, etc. Double Hump Fission Yields Light (28, 50) +, and Heavy (50,82) + Delayed Neutrons, Poisons, i.e. Xe-135 Lead-208 (82, 126) Last Stable Isotope

8 Semi-Empirical Binding, B/A 1955 Stable Isotope Data Contribution Terms

9 Mass Parabolas Odd A Decay Even A Decay

10 Questions What is the Nature of the Closed Shells? What Produces Liquid Drop Property? Why Doesn t the Semi-Empirical Binding Energy Formula Match the Low A Peaks? What is the Physical Decay Mechanism?

11 Lucas Electromagnetic Nucleus Protons and Neutrons Occupy Fixed Positions in Symmetric 3D Space Under Static Force Balance They are Distributed in 6 Double Cycles Occupying 2, 8, 18, 18, 32 and 50 Inner Neutron Shells Can Expand to Next Number Like Electron Shells

12 Lucas Electromagnetic Nucleus Density Decreases in Center for Big Nuclei Lead has Outer 50 and 32 Protons = 82, and 50, 32, 18, 18, and 8 = 126 Neutrons

13 Lucas Rule Assignments for Doubly Magic Isotopes AT A Z N N1 P1 N2 He O Ca Ca Ni Sn Sn Pb P2 N3 P N4 P4 N5 P5 N6 P

14 Lucas Electromagnetic Nucleus Magic Numbers are Composites of 6 Shells Proton Shells Fill from Outside The Neutron Shell Between Outer Proton Shells Acts Like a Decoupler by Polarizing Sideways => Liquid Drop Properties Interior Neutrons Polarize with Plus Ends Toward Center and Fill Inwards Decay is a Vibration Process!

15 Complicated Vibrations Force Laws Nonlinear Nucleons Vibrate About Positions Internal Bumped Nucleon Vibrations -> Beta Decay? Non-Spherical Rotational Vibrations Linear Model Analog of Schrödinger Equation!

16 Semi-Empirical Binding Energy B/A - K1 Volume - K2 (#Neutrons + #Protons) in outermost shell /A Surface - K3 Z(Z-1) A-4/3 Coulomb - K4 (#paired Neutrons #paired Protons)2 /A Asymmetry, Magic - K5 (#unpaired Protons + #unpaired Neutrons) /A Pairing

17 Lucas New Semi-Empirical Binding Energy for 3000 Nuclei

18 Electromagnetic Nucleus Computational Confirmation

19 Superheavy Nuclei Produced by Bombarding Heavy Elements, i.e., Uranium, Plutonium, Curium, Californium, and Berkelium by Heavy Ions Like Doubly Magic Ca-48 (20, 28) Work Done at GSI Darmstadt, JINR Dubna, ORNL, RIKEN Japan, LLNL Longest Half Lives are 12 Minutes, and 22 Seconds

20 Superheavy Nuclei Sea Extent

21 Observations Lower End of the Red Peninsula is Near Z = 90 and N = 140; Upper End of the Red Peninsula is Near Z = 100 and N = 158 Low End of the Green Peninsula Area is Near Z = 82; Upper End Around Z = 108 Shoal is Near Z = 108, and it Lies Between N = 158 and 164 Island of Stability is Centered with a Red Area Near Z = 108 and N = 182; Island Lies Between Z = 102 and 118, and Between N = 172 and N= 184.

22 Theoretical Superheavy Nuclei Magic Numbers Spherical and Deformed Nuclei, Multiple Theories, Liquid Drop Plus Shells Magic Z at 108, 110, 114, 120? Magic N at 152, 164, 172, 184? Why Not Others, Close Together?

23 Z Extension of Lucas Shells Z = = 90 Z = = 92 Z = = 100 Z = = 102 Z = = 108 Z = = 110 Z = = 118 Z = = 120

24 N Extension of Lucas Shells N = = 140 N = = 142 N = = 158 N = = 164 N = = 172 N = = 182 N = = 184

25 Consequences New N and Z Numbers Cover Other Theoretical Values Agree with Peninsula, Shoal and Island Boundaries Suggestion of Lower A Single and Double Magic Nuclei in Continent Yet Unexplored Requires a Careful Look at Isotope Data In the Table of Isotopes

26 N Extension of Lucas Shells? N = = 90 N = = 92 N = = 100 N = = 102 N = = 108 N = = 110 N = = 118 N = = 120 N = = 128

27 Further Downward Z Extension of Lucas Shells? Z = = 58 i.e. Cerium, N = 58 First Suggested in 1981 by Linus Pauling Z = = 68 i.e. Erbium, Near N = 70 by Pauling Z = = 76 i.e. Osmium

28 Linus Pauling Data

29 Isotopes Considered Peninsula Thorium Z = 90 Uranium Z = 92 Fermium Z = 100 Nobelium Z = 102 Continent Cerium Z = 58 Dysprosium Z = 66 Osmium Z = 76 Lead Z = 82

30 Thorium, Z = 90 = Holy Grail? 19 Isotopes Doubly Magic Th-230 (90, y Doubly Magic Th-232 (90, 142)@ 1.4E10 y Th-229, One Short of 7300 y N/Z ~ 1.54 for Most Stable Lighter Isotopes, ns to days Heavier Isotopes, days to minutes

31 Uranium, Z = Isotopes Doubly Magic U- 232 (92, 68 y Odd 1.6E5 y Doubly Magic U- 234 (92, 2.4E5 y 2.4E7 y 4.5E9 y and N/Z = 1.52 Lighter Isotopes, µs to days Heavier Isotopes, days to minutes

32 Neptunium and Plutonium Long Lived U, Np and Pu Isotopes All Lie at a Ratio of N/Z Near 1.54 Seaborg Criterion for Even A Spontaneous Fission Parameter Z2/A > ~ 44 Odd-A Nuclei More Stable to Spontaneous Fission than Even-A Nuclei Fission Preferred Mode of Decay for the Proton Rich Heavy and Superheavy Isotopes

33 Thorium, Uranium, Neptunium and Plutonium Conclusions N/Z ~ 1.54 Is Important Magic and Near Magic Gives Longer Half Lives Magic Gives More Isotopes Worse to Have Too Many Protons vs. Too Many Neutrons

34 Fermium, Z = Isotopes Odd 100 days Longest Lived Doubly Magic Fm-258 (100, 158), Short Spontaneous Fission Lighter Isotopes, ms to days Heavier Isotopes, days to ms

35 Nobelium, Z = Isotopes Odd 58 minutes Longest Lived Doubly Magic Fm-260 (102, 158), Short Spontaneous Fission Lighter Isotopes, ms to minutes Heavier Isotopes, ms

36 Fermium and Nobelium Conclusions Magic Effects Not As Clear Longest Lived Odd, One Short of Doubly Magic Spontaneous Fission More Important, at Doubly Magic Magic Gives More Isotopes Worse to Have Too Many Protons vs. Too Many Neutrons

37 Cerium, Z = Isotopes Ce-140, Doubly Magic at N = 82, Almost 90% of Natural Cerium Ce148, Doubly Magic at N = 56 seconds, and Ce-150 Doubly Magic at N = 4 seconds Are Among Heaviest Cerium Isotopes Known

38 Dysprosium, Z = Isotopes Dy-160 to Dy-164, Comprise Most of the Naturally Stable Isotopes Lighter Dy-158, with a Magic N = 92, and Dy-156, with a Magic N = 90, Are Also Stable Light Dy-148, with a Magic N = 3.1 minutes Heavy Dy-166, with a Magic N = 81.6 hours, and Dy-168, with a Magic N = 8.7 minutes

39 Osmium, Z = Isotopes Naturally Occurring Osmium Isotopes Lie Between Os-192 and Os-187 Among Lightest Osmium Isotopes are Os166, with a Doubly Magic N = 7.1 seconds, and Os-168, with a Doubly Magic N= 2.2 seconds Among Heaviest, Os-194, with a Doubly Magic N = 6 years, and Os-196, with a Doubly Magic N = 35 minutes

40 Lead Z = Isotopes Naturally Occurring and Long-lived Lead Isotopes Lie Between Pb-204 and Pb-208 Among Lightest Doubly Magic Lead Isotopes are Pb-202, with a Magic N= 5.2E4 years, and Pb-200, with a Magic N = 21.5 hours Among Heaviest Doubly Magic, Pb-210, with a Magic N = 22.3 years

41 Better Fission Yield Distribution With Magic 58 Double Hump Fission Yields, U n Light (28, 50), and Heavy (50, 82) = 26 to Divide? Or Better Yet Light (28, 58), and Heavy (50, 82) = 18 to Divide? Matches Small Lower Bound of 86 and Large Lower Bound of 132, and 18 Width Containing 95% of Fission Products

42 Fission Yield Distributions

43 Conclusions Magic Affects Number of Stable Isotopes Magic Accounts For Longer Half Lives and Number of Lighter and Heavier Isotopes Large Number of Isotopes Related to New Magic Numbers N/Z ~ 1.54 Are Most Stable Superheavy Half Lives Won t Be Long

44 Conclusions Table of Isotopes Is Now 4 ½ Inches Thick! Data on Isotopes: Level Schemes, Half Lives, Reactions, Abundance, etc. Probably Not Examined for Systematic Behavior Fertile Area for Research!

Nuclear Fission Fission discovered by Otto Hahn and Fritz Strassman, Lisa Meitner in 1938

Nuclear Fission Fission discovered by Otto Hahn and Fritz Strassman, Lisa Meitner in 1938 Fission Readings: Modern Nuclear Chemistry, Chapter 11; Nuclear and Radiochemistry, Chapter 3 General Overview of Fission Energetics The Probability of Fission Fission Product Distributions Total Kinetic