Nuclear Binding Energy

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Presentation transcript:

Nuclear Binding Energy Is the nucleon bounded equally to every other nucleon? C ≡ this presumed binding energy. Btot = C(A-1)  A  ½ Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … !  wrong assumption  finite range of strong force, and force saturation. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Nuclear Binding Energy Pairing Energy. Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !) Sn (A, Z, even N) – Sn (A-1, Z, N-1) This is the neutron pairing energy. even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei. Odd N Even N Total Odd Z Even Z HW 1\ Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Nuclear Physics, JU, Second Semester, 2010-2011 Neutron Excess Remember HW 1. Asymmetry Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Nuclear Binding Energy For constant Z Sn (even N) > Sn (odd N) For constant N Sp (even Z) > Sp (odd Z) Remember (Krane 3.14) in HW 6. 208Pb (doubly magic)  can then easily remove the “extra” neutron in 209Pb. Nuclear magic numbers: 2, 8, 20, 28, 50, 82,126, …(for Z or N). Lead isotopes Z = 82 208Pb Neutron Separation Energy Sn (MeV) Neutron Number N Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Abundance Systematics Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Abundance Systematics NEUTRON CAPTURE CROSS SECTION Formation process  Abundance NEUTRON NUMBER ABUNDANCE r s r s MASS NUMBER Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula von Weizsäcker in 1935. Liquid drop. Shell structure. Main assumptions: Incompressible matter of the nucleus  R  A⅓. Nuclear force saturates. Binding energy is the sum of terms: Volume term. 4. Asymmetry term. Surface term. 5. Pairing term. Coulomb term. 6. Closed shell term. ….. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Volume Term Bv = + av A Bv  volume  R3  A  Bv / A is a constant i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus. constant The other terms are “corrections” to this term. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Surface Term Bs = - as A⅔ Binding energy of inner nucleons is higher than that at the surface. Light nuclei contain larger number (per total) at the surface. At the surface there are: Nucleons. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Coulomb Term BC = - aC Z(Z-1) / A⅓ Charge density   Z / R3. W  2 R5. Why ??? W  Z2 / R. Actually: W  Z(Z-1) / R. BC / A = - aC Z(Z-1) / A4/3 Remember HW 5 … ?! Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Surface effect Coulomb effect Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Quiz 1 From our information so far we can write: For A = 125, what value of Z makes M(A,Z) a minimum? Is this reasonable…??? So …..!!!! Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Asymmetry Term Ba = - aa (A-2Z)2 / A Light nuclei: N = Z = A/2 (preferable). Deviation from this “symmetry”  less BE and stability. Neutron excess (N-Z) is necessary for heavier nuclei. Ba / A = - aa (N-Z)2 / A2. Back to this when we talk about the shell model. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Pairing Term Bp =  Extra Binding between pairs of identical nucleons in the same state (Pauli !)  Stability (e.g. -particle, N=2, Z=2). even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei. Remember HW 1\ ….?! Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that:   A-¾ . Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Closed Shell Term Bshell =  Extra binding energy for magic numbers of N and Z. Shell model. 1 – 2 MeV more binding. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Fitting to experimental data. More than one set of constants av, as ….. In what constants does r0 appear? Accuracy to ~ 1% of experimental values (BE). Atomic masses 1 part in 104. Uncertainties at magic numbers. Additional term for deformation. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

The Semi-empirical Mass Formula Variations……. Additional physics…. Fitting……(Global vs. local)….. Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).

Nuclear Physics, JU, Second Semester, 2010-2011 Work it out … Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh).