PHL424: Nuclear Shell Model - GSI
PHL424: Nuclear Shell ModelIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Themes and challenges in modern science Complexity out of simplicity – MicroscopicHow the world, with all its apparent complexity and diversity can be constructedout of a few elementary building blocks and their interactionsindividual excitationsof nucleons Simplicity out of complexity – MacroscopicHow the world of complex systems can display such remarkable regularity andsimplicityvibrationIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017rotationfission
The nuclear forceThe nuclear force is short-range, but does not allow forcompression of nuclear matter.Yukawa – potential:1 𝑉𝑉0 𝑟𝑟 𝑔𝑔𝑠𝑠 𝑒𝑒𝑟𝑟ω,ρ𝑚𝑚𝜋𝜋 𝑐𝑐 𝑟𝑟ℏπσm(π) 140 MeV/c2m(σ) 500-600 MeV/c2m(ω) 784 MeV/c2Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
The deuteronmass (MeV/c2)1875.61charge (e)1Iπ1 binding energy (MeV)2.2245magnetic moment (μN)quadrupole moment (b)np0.8574 0.8798 μN μS ( 21𝐻𝐻 ) the deuteron can not be a pure s state! 96% s and 4% d.0.0029not spherical consistent with s/d-ratio 96/4The deuteron is an ideal candidate for tests of our basic understanding of nuclear physicsIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Structure of the nuclear forceStructure of the nuclear force is more complex than e.g. Coulomb force. It results from itsstructure as residual interaction of the colorless nucleons.central force V0(r)results from deuteron properties (96% 3S1 state)spin dependent central force2𝑆𝑆 1𝐿𝐿𝐽𝐽results from neutron-proton scattering (spin-spin interaction)not central tensor forceresults from deuteron properties (4% 3D1 state)spin-orbit (ℓ·s) term2𝑆𝑆 1𝐿𝐿𝐽𝐽results from scattering of polarized protons (left/right asymmetry)𝑉𝑉 𝑟𝑟 𝑉𝑉0 𝑟𝑟1 𝑉𝑉𝑠𝑠𝑠𝑠 𝑟𝑟 𝑠𝑠1 𝑠𝑠2 2ℏ3 𝑠𝑠1 𝑥𝑥⃗ 𝑠𝑠2 𝑥𝑥⃗ 𝑉𝑉𝑇𝑇 𝑟𝑟 2 𝑠𝑠1 𝑠𝑠2ℏ𝑟𝑟 21 𝑉𝑉ℓ𝑠𝑠 𝑟𝑟 𝑠𝑠1 𝑠𝑠2 ℓ 2ℏIndian Institute of Technology Roparcentral potentialspin-spin interactiontensor forcespin-orbit interactionHans-Jürgen Wollersheim - 2017
Structure of the nuclear force1 spin-spin force: 𝑉𝑉𝑠𝑠𝑠𝑠 𝑟𝑟 𝑠𝑠1 𝑠𝑠2 /ℏ2different eigenvalues fortriplet and singlet states ⟩212 ⟩ ⟩ tensor force:3 𝑠𝑠1 𝑥𝑥⃗ 𝑠𝑠2 𝑥𝑥⃗ 𝑉𝑉𝑇𝑇 𝑟𝑟 2 𝑠𝑠1 𝑠𝑠2𝑟𝑟 2ℏsmall deformation of deuteriummaximum magnetic dipole moments ℓ·s coupling: 𝑉𝑉ℓ𝑠𝑠 𝑟𝑟 ℓ 𝑠𝑠⃗scattering of protons on polarized protonsasymmetry of counting rates-left scattering: ℓ 𝑠𝑠⃗ 0right scattering: ℓ 𝑠𝑠⃗ 0ℓ·s coupling:-no net contribution in the center of nucleusradial dependence at the surface of the nucleusIndian Institute of Technology Ropar𝑉𝑉ℓ𝑠𝑠 𝑟𝑟 1 𝑑𝑑𝑑𝑑 𝑟𝑟 𝑑𝑑𝑑𝑑Hans-Jürgen Wollersheim - 2017s 0, ℓ 1 ⟩ ⟩𝑥𝑥⃗ ⟩𝑥𝑥⃗attractive repulsives 1, ℓ 0
Many-body forcesinternal forces governing a 3He nucleusThe force on one nucleon does not only depend onthe position of the other nucleons, but also on thedistance between the other nucleons! These arecalled many-body forces.tidal effects lead to 3-body forcesin earth-sun-moon systemRemember: Nucleons are finite-mass composite particles, can be excited to resonances. Dominant contribution Δ(1232 MeV)Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
The Fermi gas modelproton potentialneutrons protonsneutron potential The Fermi gas model assumes that protons and neutrons are moving freely within thenuclear volume. They are distinguishable fermions (s ½) filling two separate potentialwells obeying the Pauli principle ( -pair).The model assumes that all fermions occupy the lowest energy states available to them tothe highest occupied state (Fermi energy), and that there is no excitation across the Fermienergy (i.e. zero temperature).The Fermi energy is common for protons and neutrons in stable nuclei.If the Fermi energy for protons and neutrons are different then the β-decay transforms onetype of nucleons into the other until the common Fermi energy (stability) is reached.Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Number of nucleon statesHeisenberg Uncertainty Principle:12 𝑥𝑥 𝑝𝑝 ℏThe volume of one particle in phase space: 2𝜋𝜋 ℏThe number of nucleon states in a volume V:𝑝𝑝𝑚𝑚𝑚𝑚𝑚𝑚 2𝑝𝑝 𝑑𝑑𝑑𝑑 𝑑𝑑3 𝑟𝑟 𝑑𝑑3 𝑝𝑝 𝑉𝑉 4𝜋𝜋 0𝑛𝑛 2𝜋𝜋 ℏ 32𝜋𝜋 ℏ 3states in phase spaceAt temperature T 0, i.e. for the nucleus in its ground state, the lowest states will be filledup to the maximum momentum, called the Fermi momentum pF. The number of these statesfollows from integration from 0 to pmax pF.𝑛𝑛 𝑝𝑝𝑉𝑉 4𝜋𝜋 0 𝐹𝐹 𝑝𝑝2 𝑑𝑑𝑑𝑑2𝜋𝜋 ℏ3𝑉𝑉 4𝜋𝜋 𝑝𝑝𝐹𝐹3 2𝜋𝜋 ℏ 3 3 𝑉𝑉 𝑝𝑝𝐹𝐹3𝑛𝑛 2 36𝜋𝜋 ℏSince an energy state can contain two fermions of the same species, we can have𝑉𝑉 𝑝𝑝𝐹𝐹𝑛𝑛 ���𝑛𝑛𝑛: 𝑁𝑁 3𝜋𝜋 2 ℏ3𝑝𝑝𝑝𝑝𝐹𝐹𝑛𝑛 is the Fermi momentum for neutrons, 𝑝𝑝𝐹𝐹 for protonsIndian Institute of Technology Ropar𝑝𝑝 3𝑉𝑉 ��𝑝𝑝𝑝𝑝𝑝: 𝑍𝑍 3𝜋𝜋 2 ℏ3Hans-Jürgen Wollersheim - 2017
Fermi momentumUse 𝑅𝑅 𝑟𝑟0 𝐴𝐴1 3 𝑓𝑓𝑓𝑓𝑉𝑉 4𝜋𝜋 3𝑅𝑅3 4𝜋𝜋 3𝑟𝑟3 0 𝐴𝐴The density of nucleons in a nucleus number of nucleons in a volume V:𝑉𝑉 𝑝𝑝𝐹𝐹34𝜋𝜋 3𝑝𝑝𝐹𝐹34𝐴𝐴 𝑟𝑟03 𝑝𝑝𝐹𝐹3𝑛𝑛 2 2 3 2 𝑟𝑟 𝐴𝐴 2 3 6𝜋𝜋 ℏ6𝜋𝜋 ℏ3 09𝜋𝜋 ℏ3two spin statesFermi momentum pF:6𝜋𝜋 2 ℏ3 𝑛𝑛𝑝𝑝𝐹𝐹 2𝑉𝑉1/39𝜋𝜋ℏ3 𝑛𝑛 4𝐴𝐴 𝑟𝑟031/39𝜋𝜋 𝑛𝑛 4𝐴𝐴1/3 ℏ𝑟𝑟0After assuming that the proton and neutron potential wells have the same radius, we find fora nucleus with n Z N A/2 the Fermi momentum pF.𝑝𝑝𝐹𝐹 𝑝𝑝𝐹𝐹𝑛𝑛 𝑝𝑝𝑝𝑝𝐹𝐹9𝜋𝜋 8Fermi energy: 𝐸𝐸𝐹𝐹 1/32𝑝𝑝𝐹𝐹2𝑚𝑚𝑁𝑁 ℏ 250 𝑀𝑀𝑀𝑀𝑀𝑀/𝑐𝑐𝑟𝑟0 33 𝑀𝑀𝑀𝑀𝑀𝑀Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017The nucleons move freely insidethe nucleus with large momentamN 938 MeV/c2 – the nucleon mass
Nucleon potentialThe difference B between the top of the well andthe Fermi level is the average binding energy pernucleon B/A 7 – 8 MeV. The depth of the potential V0 and the Fermienergy are independent of the mass number A:𝑉𝑉0 𝐸𝐸𝐹𝐹 𝐵𝐵𝐵 40 𝑀𝑀𝑀𝑀𝑀𝑀Heavy nuclei have a surplus of neutrons. Since the Fermi level of the protons and neutrons ina stable nucleus have to be equal (otherwise the nucleus would enter a more energeticallyfavorable state through β-decay) this implies that the depth of the potential well as it isexperienced by the neutron gas has to be larger than of the proton gas.Protons are therefore on average less strongly bound in nuclei than neutrons. This may beunderstood as a consequence of the Coulomb repulsion of the charged protons and leads to anextra term in the potential:𝑉𝑉𝐶𝐶 𝑍𝑍 1Protonen: 33MeV 7MeV, Neutronen: 43MeV 7 MeVIndian Institute of Technology Ropar𝛼𝛼 ℏ𝑐𝑐𝑅𝑅Hans-Jürgen Wollersheim - 2017
The Fermi gas model and the neutron starAssumption: neutron star as cold neutron gas with constant density- 1.5 sun masses: M 3·1030 kg (mN 1.67·10-27 kg), number of neutrons: n 1.8·1057Fermi momentum pF for cold neutron gas:9𝜋𝜋 𝑛𝑛𝑝𝑝𝐹𝐹 41/3 ℏ𝑅𝑅R is the radius of the neutron starAverage kinetic energy per neutron:9𝜋𝜋 𝑛𝑛3 𝑝𝑝𝐹𝐹2𝐸𝐸𝑘𝑘𝑘𝑘𝑘𝑘 𝑁𝑁45 2𝑚𝑚𝑁𝑁2/3𝐶𝐶3ℏ21 2 2𝑅𝑅10 𝑚𝑚𝑁𝑁 𝑅𝑅Gravitational energy of a star with constant density has an average potential energy per neutron:𝐷𝐷3 𝐺𝐺 𝑛𝑛 𝑚𝑚𝑛𝑛2𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 𝑁𝑁𝑅𝑅𝑅𝑅5Minimum total energy per neutron:𝑑𝑑𝑑𝑑𝐸𝐸/𝑁𝑁 𝐸𝐸 /𝑁𝑁 𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 /𝑁𝑁𝑑𝑑𝑑𝑑 𝑘𝑘𝑘𝑘𝑘𝑘𝑑𝑑𝑑𝑑2𝐶𝐶 𝐷𝐷𝑑𝑑 𝐶𝐶 𝐷𝐷 0𝑅𝑅3 𝑅𝑅 2𝑑𝑑𝑑𝑑 𝑅𝑅2 𝑅𝑅2𝐶𝐶𝑅𝑅 𝐷𝐷 𝑚𝑚3𝑘𝑘𝑘𝑘 𝑠𝑠 2 0ℏ2 9𝜋𝜋/4 2/3𝑅𝑅 3𝐺𝐺 𝑚𝑚𝑁𝑁 𝑛𝑛1/3Indian Institute of Technology Ropar𝐺𝐺 6.67 10 11Hans-Jürgen Wollersheim - 2017radius of a neutron star 10.7 km
Shell structure in nucleiDeviations from the Bethe-Weizsäcker mass formula:B/A (MeV per nucleon)NeutronProton2828505082especially stable:42He216812682O84020Ca204820Ca2820882mass number AIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017Pb126
Shell structure in nuclei deviations from the Bethe-Weizsäcker mass formula: large binding energies208Pb132SnIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
2-neutron binding energies 2-neutron separation energies25𝑆𝑆2𝑛𝑛 𝐵𝐵𝐵𝐵 𝑁𝑁, 𝑍𝑍 𝐵𝐵𝐵𝐵 𝑁𝑁 2, 𝑍𝑍N 822321N 126S(2n) MeV19171513Sm1195BaN 84752566064687276PbSn8084889296Neutron NumberIndian Institute of Technology RoparHfHans-Jürgen Wollersheim - 2017100104108112116120124128132
Shell structure in nuclei𝐸𝐸2 1Nuclei with magic numbersof neutrons/protons high energies of the first excited 2 state small nuclear deformationstransition probabilities measured in single particle units (spu)𝐵𝐵 𝐸𝐸𝐸; 21 0 Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Shell structure in nuclei𝐸𝐸2 1Maria Goeppert-Mayer𝐵𝐵 𝐸𝐸𝐸; 21 0 J. Hans D. JensenIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Nuclear potential𝐴𝐴𝐴𝐴𝑖𝑖 1𝑖𝑖 𝑗𝑗𝑝𝑝̂ 𝑖𝑖2 𝐻𝐻 𝑉𝑉 𝑟𝑟𝑖𝑖 , � 𝑖𝑖2 𝐻𝐻 𝑉𝑉 𝑟𝑟𝑖𝑖2𝑚𝑚𝑖𝑖𝑖𝑖 1𝐴𝐴𝐴𝐴𝑖𝑖 𝑗𝑗𝑖𝑖 1 𝑉𝑉 𝑟𝑟𝑖𝑖 , 𝑟𝑟𝑗𝑗 𝑉𝑉 𝑟𝑟𝑖𝑖ℏ2 2 𝑉𝑉 𝑟𝑟 𝜀𝜀 Ψ 𝑟𝑟 02𝑚𝑚Ψ 𝑟𝑟 𝑢𝑢ℓ 𝑟𝑟 𝑌𝑌ℓ𝑚𝑚 𝜗𝜗, 𝜑𝜑 Χ 𝑚𝑚𝑠𝑠𝑟𝑟In the average nuclear potential V(r):a) harmonic oscillatorb) square well potentialc) Woods-Saxon potentialthe nucleons move freelyIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017 𝑉𝑉0𝑉𝑉 𝑟𝑟 1 𝑒𝑒 𝑟𝑟 𝑅𝑅0 𝑎𝑎
Nuclear shell model𝐴𝐴𝑝𝑝̂ 𝑖𝑖2 𝐻𝐻 𝑉𝑉 r𝑖𝑖 16 ωV5 ω0r4 ω3 ω2 ωV01 ω0 ωIndian Institute of Technology Roparsquare-wellpotential168realistic potential spin-orbit 82s1d25028201p81s2Hans-Jürgen Wollersheim - /23p3/21f5/21f7/22g1/21d3/21d5/21p1/21p3/21s1/2
Woods-Saxon potential Woods-Saxon does not reproduce the correct magic numbers(2, 8, 20, 40, 70, 112, 168)WS (2, 8, 20, 28, 50, 82, 126)exp Meyer und Jensen (1949): strong spin-orbit interactionℏ2 2 𝑉𝑉 𝑟𝑟 𝑉𝑉ℓ𝑠𝑠 𝑟𝑟 ℓ 𝑠𝑠⃗ 𝜀𝜀 Ψ 𝑟𝑟 02𝑚𝑚𝑉𝑉ℓ𝑠𝑠 𝑟𝑟 𝜆𝜆 𝑠𝑠⃗1 𝑑𝑑𝑑𝑑 𝑟𝑟 �𝜆𝜆 0dV (r )drV (r )ℓThe spin-orbit term has its origin in the relativistic description of the single particle motion inside the nucleusIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017r
Woods-Saxon potential (jj-coupling)𝚥𝚥⃗ ℓ 𝑠𝑠⃗1 𝑗𝑗 2 ℓ2 𝑠𝑠 2 ℏ221 𝑗𝑗 𝑗𝑗 1 ℓ ℓ 1 𝑠𝑠 𝑠𝑠 1 ℏ22 ℓ 𝑠𝑠 The nuclear potential with spin-orbit term:𝑉𝑉 𝑟𝑟 ℓ 𝑉𝑉2 ℓ𝑠𝑠𝑉𝑉 𝑟𝑟 𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2ℓ 1𝑉𝑉ℓ𝑠𝑠2𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2spin-orbit interaction leads to a large splitting for large ℓ.𝑗𝑗 ℓ 1/2Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017𝑗𝑗 ℓ 1/2𝑗𝑗 ℓ 1/2 ℓ 1 /2 𝑉𝑉ℓ𝑠𝑠ℓ/2 𝑉𝑉ℓ𝑠𝑠
Woods-Saxon potentialThe spin-orbit termℓ 1/2ℓ 1/2 lowers the j ℓ 1/2 orbital from thehigher oscillator shell (intruder states) reproduces the magic numbers 𝐸𝐸ℓ𝑠𝑠 2ℓ 1 2 ℏ 𝑉𝑉ℓ𝑠𝑠2large energy gaps very stable nucleiImportant consequences: lowering orbitals from higher lying N 1 shellhaving different parity than orbitals from the N shell strong interaction preserves the parity. The lowered orbitalswith different parity are rather pure states and do not mixwithin the shellIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Shell model – mass dependence of single-particle energies Mass dependence of the neutronenergies: 𝐸𝐸 𝑅𝑅 2 number of neutrons in each level:2 2ℓ 1Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Success of the extreme single-particle shell model Ground state spin and parity:Every orbital has 2j 1 magnetic sub-states,completely filled orbitals have spin J 0,they do not contribute to the nuclear spin.For a nucleus with one nucleon outside acompletely occupied orbital the nuclear spinis given by the single nucleon.nℓj J(-)ℓ πIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Success of the extreme single-particle shell model Magnetic moments:The g-factor gj is given by:with ℓ2 𝚥𝚥⃗ 𝑠𝑠⃗2𝜇𝜇𝑗𝑗 𝑔𝑔ℓ ℓ 𝑔𝑔𝑠𝑠 𝑠𝑠⃗ 𝑔𝑔𝑗𝑗 𝚥𝚥⃗ 𝚥𝚥⃗2 2 𝚥𝚥⃗ 𝑠𝑠⃗ 𝑠𝑠⃗ 2𝜇𝜇⃗𝑗𝑗 𝑠𝑠⃗ 2 𝚥𝚥⃗ ℓ2 𝜇𝜇𝑗𝑗 𝚥𝚥⃗2 2 𝚥𝚥⃗ ℓ ℓ2𝑔𝑔ℓ ℓ 𝑔𝑔𝑠𝑠 𝑠𝑠⃗ 𝚥𝚥⃗𝚥𝚥⃗ 𝑗𝑗𝑗𝑗𝑔𝑔ℓ 𝑗𝑗 𝑗𝑗 1 ℓ ℓ 1 3/4 𝑔𝑔𝑠𝑠 𝑗𝑗 𝑗𝑗 1 ℓ ℓ 1 3/4 𝚥𝚥⃗2 𝑗𝑗 𝑗𝑗 1𝑔𝑔𝑗𝑗 11 ℓ ℓ 1 𝑠𝑠 𝑠𝑠 1 𝑔𝑔ℓ 𝑔𝑔𝑠𝑠 𝑔𝑔ℓ 𝑔𝑔𝑠𝑠222𝑗𝑗 𝑗𝑗 1Simple relation for the g-factorof single-particle states𝜇𝜇𝑔𝑔𝑠𝑠 𝑔𝑔ℓ ��𝑛𝑛𝑛 𝑔𝑔ℓ 𝜇𝜇𝑁𝑁2ℓ 1nucleus state𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017Jπμ/μNmodel experiment
Success of the extreme single-particle shell model magnetic moments:𝜇𝜇𝑧𝑧11 𝑔𝑔𝑠𝑠 𝜇𝜇𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/222 31𝑗𝑗 𝑔𝑔ℓ 𝑗𝑗 𝑔𝑔𝑠𝑠 𝜇𝜇𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/222𝑗𝑗 1𝑔𝑔ℓ 𝑗𝑗 g-factor of nukleons:proton:gℓ 1; gs 5.585neutron: gℓ 0; gs -3.82proton:neutron:Indian Institute of Technology Ropar𝜇𝜇𝑧𝑧 𝜇𝜇𝑧𝑧𝑗𝑗 2.293 𝜇𝜇𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2𝑗𝑗𝑗𝑗 2.293 𝜇𝜇𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2𝑗𝑗 1 𝑁𝑁 1.91 𝜇𝜇𝑁𝑁 𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2𝑗𝑗 𝜇𝜇𝑓𝑓𝑓𝑓𝑓𝑓 𝑗𝑗 ℓ 1/2 1.91 𝑗𝑗 1 𝑁𝑁Hans-Jürgen Wollersheim - 2017
Magnetic moments: Schmidt linesmagnetic moments: protonmagnetic moments: neutronIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
The three structures of the shell modelIndian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Systematics of the Te isotopes (Z 52)Neutron number6870727476788082Val. Neutr. number 14121086420Indian Institute of Technology RoparHans-Jürgen Wollersheim - 2017
Indian Institute of Technology Ropar Hans-Jürgen Wollersheim - 2017 Structure of the nuclear force Structure of the nuclear force is more complex than e.g. Coulomb force. It results from its structure as residual interaction of the colorless nucleons. central force V 0 (r) spin dependent central force . not central tensor force . spin-orbit .
Shell Donax TU Shell Spirax S6 ATF UM Shell Donax TV Shell Spirax S6 ATF VM Shell Donax TX Shell Spirax S4 ATF HDX* Shell ATF XTR Shell Donax TA Shell Spirax S2 ATF D2 Shell ATF IID GREASES Shell Retinax CSZ Shell Gadus S4 V45AC Shell Albida HDX Shell Gadus S3 V460D Shell Retinax LX2 Shell
Indian Institute of Technology Ropar Hans-Jürgen Wollersheim - 2017 PHL424: Nuclear angular momentum n 1 . n 3 . n 2 . electron orbitals . quantum numbers: n (principal) 1,2,3,
Bash Shell The shell of Linux Linux has a variety of different shells: – Bourne shell (sh), C shell (csh), Korn shell (ksh), TC shell (tcsh), Bour ne Again shell (bash). Certainly the most popular shell is “bash”. Bash is an sh-compatible shell that incorporates useful features from the Korn shell (ksh) and C
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Shell TelluS S2 V 15 15 3.8 160 –42 871 Shell TelluS S2 V 22 22 4.8 190 –39 872 Shell TelluS S2 V 32 32 6.4 170 –42 872 Shell TelluS S2 V 46 46 8.2 210 –39 872 Shell TelluS S2 V 68 68 10.9 230 –36 877 Shell TelluS S2 V 100 100 14.7 176 –30 889 Shell TelluS S3 M 46 46 6.8 220 –33 865 Shell TelluS S4 Vx 32 33.8 9.93 100 –60 866
What is a Shell Script or shell scripting 13 Why shell scripting 14 Chapter 1 Challenges 16 Chapter 2: Getting Started With Shell Programming 17 The bash shell 17 Shell commands 19 The role of shells in the Linux environment 21 Other standard shells 23 Hello, World! Tutorial 25 Shebang 27 Shell Comments 29 Setting up permissions on a script 30
Nuclear Chemistry What we will learn: Nature of nuclear reactions Nuclear stability Nuclear radioactivity Nuclear transmutation Nuclear fission Nuclear fusion Uses of isotopes Biological effects of radiation. GCh23-2 Nuclear Reactions Reactions involving changes in nucleus Particle Symbol Mass Charge
Academic writing introductions tips with useful phrases Start the introduction by answering the question which you have been set or you have set yourself (“I believe that the government’s policy on ” etc). Start the introduction by setting out the background to the question that you have been set or have set yourself (“In our globalised society, ”, “Over the last few years .
