PHGN 422: Nuclear Physics - Inside Minesinside.mines.edu/~kleach/PHGN422/lectures/Lecture1.pdf ·...

P H G N 4 2 2 : N U C L E A R P H Y S I C S

PHGN 422: Nuclear PhysicsLecture 1: General Introduction to Nuclear Physics

Prof. Kyle Leach

August 27, 2019

Slide 1


Course Goals and Objectives

• Introduction to subatomic physics focused on the atomic nucleus.• Characterization and systematics of nuclear states, symmetries,

and shapes.• Introduction to the electromagnetic, weak, and strong

interactions through nuclear decay.

• Providing the student with a complete backgroundunderstanding of nuclear physics for future applications

http://inside.mines.edu/NSE-home

http://electroweak.mines.edu

Slide 2 — Prof. Kyle Leach — PHGN 422: Nuclear Physics


Course Expectations

• Students should have a basic understanding of modern physics,quantum mechanics, and their applications

Source: xkcd.com



Course Expectations• Do your best to keep up with the readings and lecture review, the

textbooks are there to help...and are an excellent resource.

• Recommended TextbookIntroductory Nuclear Physics,1st EditionKenneth S. Krane

• Supplemental TextbookBasic Ideas and Concepts inNuclear Physics, 3rd EditionKris Heyde



Course Information

• Office: CoorsTek 310

• email: [email protected]• Nearly all of my research is performed at accelerator laboratories

outside of the United States, so I’m not always here. Email is thebest way to get a hold of me.

• Office Hours: Tuesday, Wednesday, and Thursday 9-11 am.• Still best to email me to let me know you’ll be coming to office

hours on a given week if you know in advance.

• Course Website: inside.mines.edu/∼kleach/PHGN422• The syllabus, lecture slides, assignments, and supplemental

material will be uploaded to this page.• You’ll still need to take notes, problems and work done on the

chalkboard are the student’s responsibility



Course Evaluation

• Assignments - 40%• Four assignments will be given in total, each worth 10% of the final

grade• They will be designed to comprehensively cover all material

presented in the course

• Midterm Examination - 30%• One midterm exam covering the first portion of the course

• Final Presentation - 30%• Students will be required to make a research presentation (10

minutes + 2 minutes question) on a nuclear physics topic of theirchoice

• Topics will be chosen after the midterm• Final two weeks of the course will in-class be presentations



So...Where Do We Start?

We need a point of reference to start discussing nuclear physics.



Distance and Energy Scales in Physics

Source: Department of Physics, Princeton University



Distance and Energy Scales in Physics



The Atom

Atom is a neutral system

Electrons

Nucleus

∼ 10−10 m = A

Atomic excitations:∼ 1-105 eV

Caused by transitionsbetween electronic states



The Atomic Nucleus

++

+

+Proton (π)

Neutron (ν)

∼ 10−15 m = fm

Nuclear excitations:∼ 105-108 eV

Caused by transitionsbetween nuclear states

Interactions can be thought of aseither microscopic or collective



Inside the Atomic Nucleus

+

Proton

Positive Charge

Mass= 938.27 MeV/c2Neutron

Neutral Charge

Mass= 939.56 MeV/c2



Protons and Neutrons

In fact, protons and neutrons are so similar, they can be classified asthe same object; The Nucleon

• They are spin 1/2 Fermions

• Radius: r ∼ 1× 10−15 m, or 1 fm (fermi)

• Charge:

• p→ +e• n→ 0

• Mass:

• p→ 938.27 MeV/c2

• n→ 939.56 MeV/c2





Nucleons are (of course) quantum mechanical objects:



• Charge:

• p→ +e• n→ 0

• Mass:

• p→ 938.27 MeV/c2

• n→ 939.56 MeV/c2








• Charge:• p→ +e• n→ 0

• Mass:

• p→ 938.27 MeV/c2

• n→ 939.56 MeV/c2









• Mass:• p→ 938.27 MeV/c2

• n→ 939.56 MeV/c2









• Mass:• p→ 938.27 MeV/c2

• n→ 939.56 MeV/c2

We will discuss the nuclear radius in the next lecture, but for now let’slook at some properties of the nucleon.



Nucleons and Isospin

+

Proton Neutron



Nucleons and Isospin

Isospin: t = 1/2

Nucleon|p〉 = | − 1/2〉

Nucleon|n〉 = |+ 1/2〉



The Structure of Nucleons

u u

d

u d

d

Protonu,u,d

< 10−18 m

Neutronu,d,d

Particle excitations:> 109 eV

“Up” (u)m = 2.4 MeV/c2

q = +2/3

“Down” (d)m = 4.8 MeV/c2

q = −1/3



Elementary Particles of the Standard Model



The “History” of Subatomic Physics



Back to the Atomic Nucleus

++

+

+Proton (π)

Neutron (ν)

∼ 10−15 m = fm

Nuclear excitations:∼ 105-108 eV

Caused by transitionsbetween nuclear states

Interactions can be thought of aseither microscopic or collective



Terminology

Nuclei are typically referred to by the number of nucleons (protonsand neutrons) that they contain:

A = N + Z

The number of protons defines the chemical symbol, and is alsoreferred to as the nuclear charge



Terminology


A = N + Z

• Number of Neutrons




Terminology


A = N + Z

• Number of Neutrons • Number of Protons




Typical Notation

AZXN

• A is the number of nucleons, or the nuclear mass

• X is the chemical symbol, as used in the periodic table, and isdefined by the nuclear charge Z

• Therefore, N and Z are often omitted, since all of the relevantinformation can be defined by A and X



Typical Notation

AZXN

• A is the number of nucleons, or the nuclear mass

• X is the chemical symbol, as used in the periodic table, and isdefined by the nuclear charge Z

• Therefore, N and Z are often omitted, since all of the relevantinformation can be defined by A and X

AXSlide 20 — Prof. Kyle Leach — PHGN 422: Nuclear Physics


Example

What is the notation for a nucleus with Z = 30 and N = 32(ie. 30 protons and 32 neutrons)?

• What is the chemical symbol for an element with Z = 30?• Now include the number of neutrons (recall: A = N + Z)• And finally, into more standard notation:



Example


• What is the chemical symbol for an element with Z = 30?

• Now include the number of neutrons (recall: A = N + Z)• And finally, into more standard notation:



ExampleWhat is the notation for a nucleus with Z = 30 and N = 32

(ie. 30 protons and 32 neutrons)?• What is the chemical symbol for an element with Z = 30?




Example




30Zn



Example



• Now include the number of neutrons (recall: A = N + Z)

• And finally, into more standard notation:



Example



• Now include the number of neutrons (recall: A = N + Z)


6230Zn32



Example


• What is the chemical symbol for an element with Z = 30?• Now include the number of neutrons (recall: A = N + Z)




Example


• What is the chemical symbol for an element with Z = 30?• Now include the number of neutrons (recall: A = N + Z)


62ZnSo, we end with the mass-62 zinc nucleus. As most nuclear

physicists are a bit cavalier with the term “mass”, so let’s briefly clarifywhat we mean.



The Atomic Mass Unit (a.m.u. or u)

The atomic mass unit is defined by the mass of 126 C6, such that its

mass in a.m.u is exactly 12.

1 u =1

12· m(12C) (1)

• Unit Conversions:

• 1 u = 931.494 MeV/c2 (most common for our purposes)• Recall: E = mc2

• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2

• 1 u = 1.660× 10−27 kg• Also referred to as a Dalton (although very rarely...). 1 u = 1 Da






1 u =1

12· m(12C) (1)

† Note: this is not, in general, true for any other nucleus. The nuclear (atomic) mass isnot simply the sum of its constituent nucleons. One must account for the binding

energy to obtain the nuclear (atomic) mass. This will be discussed next week.

• Unit Conversions:

• 1 u = 931.494 MeV/c2 (most common for our purposes)• Recall: E = mc2

• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2







1 u =1

12· m(12C) (1)



• Unit Conversions:• 1 u = 931.494 MeV/c2 (most common for our purposes)

• Recall: E = mc2

• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2







1 u =1

12· m(12C) (1)



• Unit Conversions:• 1 u = 931.494 MeV/c2 (most common for our purposes)• Recall: E = mc2

• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2







1 u =1

12· m(12C) (1)




• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2

• 1 u = 1.660× 10−27 kg

• Also referred to as a Dalton (although very rarely...). 1 u = 1 Da






1 u =1

12· m(12C) (1)




• mp = 938.27 MeV/c2

• mn = 939.56 MeV/c2

• me = 0.511 MeV/c2




How We Organize Nuclei

We need to find a convenient way to classify nuclei with differentnumbers of protons and neutrons.

• We know that atomic systems are organized by the number ofelectrons (and their orbital shells) in the Periodic Table.

• This model will not work for nuclei since the classificationcharacteristics are very different. Also, there are severalthousand nuclei that need to be classified.†Aside: There are roughly 3000 known (experimentally observed) nuclei in the universe. Recent predictions suggest that there

may be more than 7000 bound nuclear systems that are able to exist....

• Typically, these classifications are done by neutron and protonnumber, and nuclei are arranged in what we call:

The Nuclear Chart or The Nuclear Landscape.









The Nuclear Chart or The Nuclear Landscape.

†J. Erler et al., Nature 486, 509512 (2012)









The Nuclear Chart or The Nuclear Landscape.†J. Erler et al., Nature 486, 509512 (2012)



The Nuclear Chart

Phil Walker, New Scientist Magazine, October 2011



Navigating the Nuclear Chart• Stable Nucleus - A nuclear system that does not undergo

radioactive decay (ie. it is energetically unfavourable). Thisregion of the nuclear chart is often called the Valley of Stability orLine of Stability.

• Radioactive Nucleus (or unstable) - A nucleus that isspontaneously able to decrease its total energy by emmittingionizing radiation. This may result in a change in the totalnumber of protons and neutrons.

• Neutron-Rich Nucleus - A nucleus that has an excess ofneutrons relative to the stable isotope for a given Z. This is to theright of the valley of stability.

• Neutron-Deficient Nucleus (also: Proton-Rich) - A nucleus thathas an excess of protons relative to the stable isotope for a givenZ. This is to the left of the valley of stability.

• The Driplines (proton and neutron) - The limits of the nuclearchart where bound nuclei can no longer exist. On the far left isthe proton dripline and the far right is the neutron dripline.



Isotopes, Isotones, and Isobars

• Isotope:

Nuclei with the same number of protons (Z), but a different numberof neutrons (N) and a different mass (A)

• Isotone:

Nuclei with the same number of neutrons (N), but a differentnumber of protons (Z) and a different mass (A)

• Isobar:

Nuclei with the same number of nucleons (mass? not really...) (A),but a different number of protons (Z) and neutrons (N)




• Isotope:Nuclei with the same number of protons (Z), but a different numberof neutrons (N) and a different mass (A)

• Isotone:

Nuclei with the same number of neutrons (N), but a differentnumber of protons (Z) and a different mass (A)

• Isobar:






• Isotone:Nuclei with the same number of neutrons (N), but a differentnumber of protons (Z) and a different mass (A)

• Isobar:






• Isotone:Nuclei with the same number of neutrons (N), but a differentnumber of protons (Z) and a different mass (A)

• Isobar:Nuclei with the same number of nucleons (mass? not really...) (A),but a different number of protons (Z) and neutrons (N)



The Nuclear Chart

Phil Walker, New Scientist Magazine, October 2011



Interesting Features of the Nuclear Chart

The nuclear chart can reveal some interesting effects based on whatwe (as a community) have observed over several decades. Thefollowing is just a brief taste of what we will explore over the next 16weeks....



Interesting Features of the Nuclear ChartExample: Energy required to remove two neutrons from a nucleus

Two-neutron separation energies (S2n ), http://www.nndc.bnl.gov



Interesting Features of the Nuclear ChartExample: Energy required to remove two protons from a nucleus

Two-proton separation energies (S2p ), http://www.nndc.bnl.gov



Interesting Features of the Nuclear ChartExample: The binding energy per nucleon (ie. BE/A)

Nuclear binding energies (per nucleon) (BE/A), http://www.nndc.bnl.gov



Interesting Features of the Nuclear ChartExample: Energy released (or required) in α decay

Alpha decay Q value (Qα ), http://www.nndc.bnl.gov



Applications of Nuclear Physics

Since nuclei close to each other often have similar characteristics, wecan also take a brief look at which regions of the nuclear chart arerelevant for various forms of physics and engineering.



Nuclear Astrophysics

Source: The Facility for Rare Isotope Beams (FRIB)



Nuclear Fission: Energy and Engineering

http://www.nndc.bnl.gov



Our World for the Next 16 Weeks...

J. Erler et al., Nature 486, 509512 (2012)



Next Class...

Reading Before Next Class

• Introduction and Chapter 1 of Krane

Next Class Topics

• The fundamental interactions of nature

• The strong nuclear force and nuclear binding


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