Finding Magic Numbers for Heavy and Superheavy Nuclei By Roger A. - - PowerPoint PPT Presentation

Finding Magic Numbers for Heavy and Superheavy Nuclei

By Roger A. Rydin Associate Professor Emeritus of Nuclear Engineering

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, Semi-

Empirical Binding Energy Formula

Disturbed by Fast Moving Nucleons in

Nucleus, Coulomb Barrier Penetration

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

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

Order of Presentation

• 1. Robley Evan’s 1950s Nuclear Physics for

Engineers

• 2. Magic Numbers and the Semi-Empirical

Binding Energy Formula

• 3. Lucas’ Electromagnetic Model of the

Nucleus

• 4. Superheavy Nuclei
• 5. New Magic Proton and Neutron Numbers
• 6. Consequences for Selected Isotopes

The Atomic Nucleus - 1955

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

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

Semi-Empirical Binding, B/A 1955

Stable Isotope Data Contribution Terms

Mass Parabolas

Odd A Decay Even A Decay

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 ?

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

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

Lucas’ “Rule” Assignments for Doubly Magic Isotopes

AT A Z N N1 P1 N2 P2 N3 P3 N4 P4 N5 P5 N6 P6 He 4 2 2 2 2 O 16 8 8 8 8 Ca 40 20 20 6 6 14 14 Ca 48 20 28 2 8 6 18 14 Ni 48 28 20 2 6 8 14 18 Sn 100 50 50 18 18 32 32 Sn 132 50 82 6 8 18 18 18 32 32 Pb 208 82 126 8 18 18 32 32 50 50

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 !

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 !

Semi-Empirical Binding Energy

B/A - K1 Volume

• K2 (#Neutrons + #Protons) in
• utermost 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

Lucas’ New Semi-Empirical Binding Energy for 3000 Nuclei

Electromagnetic Nucleus Computational Confirmation

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

Superheavy Nuclei Sea Extent

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.

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 ?

Z Extension of Lucas’ Shells

• Z = 50 + 32 + 8 = 90
• Z = 50 + 32 + 8 + 2 = 92
• Z = 50 + 32 + 18 = 100
• Z = 50 + 32 + 18 + 2 = 102
• Z = 50 + 32 + 18 + 8 = 108
• Z = 50 + 32 + 18 + 8 + 2 = 110
• Z = 50 + 32 + 18 + 18 = 118
• Z = 50 + 32 + 18 + 18 + 2 = 120

N Extension of Lucas’ Shells

N = 50 + 32 + 32 + 18 + 8 = 140 N = 50 + 32 + 32 + 18 + 8 + 2 = 142 N = 50 + 50 + 32 + 18 + 8 = 158 N = 50 + 50 + 32 + 32 = 164 N = 50 + 50 + 32 + 32 + 8 = 172 N = 50 + 50 + 32 + 32 +18 = 182 N = 50 + 50 + 32 + 32 +18 + 2 =

184

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

N Extension of Lucas’ Shells ?

• N = 50 + 32 + 8 = 90
• N = 50 + 32 + 8 + 2 = 92
• N = 50 + 32 + 18 = 100
• N = 50 + 32 + 18 + 2 = 102
• N = 50 + 32 + 18 + 8 = 108
• N = 50 + 32 + 18 + 8 + 2 = 110
• N = 50 + 32 + 18 + 18 = 118
• N = 50 + 32 + 18 + 18 + 2 = 120

N = 50 + 32 + 18 + 18 + 8 + 2 = 128

Further Downward Z Extension

• f Lucas’ Shells ?
• Z = 32 + 18 + 8 = 58

i.e. Cerium, N = 58 First Suggested in 1981 by Linus Pauling

• Z = 32 + 18 + 18 = 68

i.e. Erbium, Near N = 70 by Pauling

• Z = 32 + 18 + 18 + 8 = 76
• i.e. Osmium

Linus Pauling Data

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

Thorium, Z = 90 = Holy Grail ?

19 Isotopes Doubly Magic Th-230 (90, 140) @ 75000 y Doubly Magic Th-232 (90, 142)@ 1.4E10 y Th-229, One Short of Double @ 7300 y N/Z ~ 1.54 for Most Stable Lighter Isotopes, ns to days Heavier Isotopes, days to minutes

Uranium, Z = 92

20 Isotopes Doubly Magic U- 232 (92, 140) @ 68 y Odd U-233 @ 1.6E5 y Doubly Magic U- 234 (92, 142) @ 2.4E5 y U-236 @ 2.4E7 y U-238 @ 4.5E9 y and N/Z = 1.52 Lighter Isotopes, µs to days Heavier Isotopes, days to minutes

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

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

Fermium, Z = 100

19 Isotopes Odd Fm-257 @ 100 days Longest Lived Doubly Magic Fm-258 (100, 158), Short

Spontaneous Fission

Lighter Isotopes, ms to days Heavier Isotopes, days to ms

Nobelium, Z = 102

12 Isotopes Odd No-259 @ 58 minutes Longest Lived Doubly Magic Fm-260 (102, 158), Short

Spontaneous Fission

Lighter Isotopes, ms to minutes Heavier Isotopes, ms

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

Cerium, Z = 58

20 Isotopes Ce-140, Doubly Magic at N = 82, Almost

90% of Natural Cerium

Ce148, Doubly Magic at N = 90, @ 56

seconds, and Ce-150 Doubly Magic at N = 92 @ 4 seconds Are Among Heaviest Cerium Isotopes Known

Dysprosium, Z = 66

30 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 = 82 @ 3.1

minutes

Heavy Dy-166, with a Magic N = 100 @

81.6 hours, and Dy-168, with a Magic N = 102 @ 8.7 minutes

Osmium, Z = 76

30 Isotopes Naturally Occurring Osmium Isotopes Lie

Between Os-192 and Os-187

Among Lightest Osmium Isotopes are Os-

166, with a Doubly Magic N = 90 @ 7.1 seconds, and Os-168, with a Doubly Magic N= 92 @ 2.2 seconds

Among Heaviest, Os-194, with a Doubly

Magic N = 118 @ 6 years, and Os-196, with a Doubly Magic N = 120 @ 35 minutes

Lead Z = 82

33 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= 120 @ 5.2E4 years , and Pb-200, with a Magic N = 118 @ 21.5 hours

Among Heaviest Doubly Magic, Pb-210,

with a Magic N = 128 @ 22.3 years

Better Fission Yield Distribution With Magic 58

Double Hump Fission Yields , U-235 + n

Light (28, 50), and Heavy (50, 82) + 14 + 12 = 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

Fission Yield Distributions

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

Conclusions

Table of Isotopes Is Now 4 ½ Inches

Thick !

Data on 3000+ Isotopes:

Level Schemes, Half Lives, Reactions, Abundance, etc.

Probably Not Examined for

Systematic Behavior

Fertile Area for Research !