PHYS 3446 – Lecture #7Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Assignment 4 due Mon. 10/11Slide Number 15Slide Number 16Slide Number 17Slide Number 18Classical and Quantum DistributionsQuantum DistributionsFermi-Dirac StatisticsFermi-Dirac StatisticsSlide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Wednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 1PHYS 3446 – Lecture #7Wednesday, Sep. 29 2010Dr. Brandt1. Nature, Range, and potential of Nuclear Force2. *** everyone should come to lab on Fri.(extra half lecture)***3. HW due4. Extra credit problem 1.4 for HW 2 due Fri.Wednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 2• Scattering experiments help to– Determine the properties of nuclei– Provide more details on the characteristics of the nuclear force• From what we have learned, it is clear that there is no classical analog to nuclear force– Gravitational force is too weak to provide the binding– Can’t have an electromagnetic origin • Deuteron nucleus has one neutron and one proton • Coulomb force destabilizes the nucleus Nature of the Nuclear ForceWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 3• Atomic structure/periodic table is well explained by the electromagnetic interaction– Implies that the range of nuclear force cannot be much greater than the radius of the nucleus– Nuclear force should range ~ 10-13– 10-12cm• Binding energy is ~constant per nucleon (observed to be about 8 MeV), essentially independent of the size of the nucleus– If the nuclear force were long-ranged, like the Coulomb force then for A nucleons, there would be ½ A(A-1) pair-wise interactions– Thus, the BE, which reflects all possible interactions among the nucleons, would grow as a function of AShort-range Nature of the Nuclear Force( 1)B AA∝−For large AconstantBBE AA= ∝≠XXXXXWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 4• Long-range nature of nuclear force is contradicted by the experimental measurement that the BE/nucleon stays constant– Nuclear force must saturate– Any given nucleon can only interact with a finite number of nucleons in its vicinity• What does adding more nucleons to a nucleus do?– Increases the size of the nucleus (for coulomb attraction, would expect more tightly bound so size would be ~ constant)• Recall that R ~ A1/3– The size of a nucleus grows slowly with A and keeps the nuclear density constant ⇒Further supports short-range nature of nuclear forceShort-range Nature of the Nuclear ForceWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 5• We can express this behavior in terms of a square-well potential– For low energy particles, the repulsive core can be ignored, why?• they don’t reach the core• This model is too simplistic, since there are too many abrupt changes in potential.– Also ignores Coulomb effectsShape of the Nuclear PotentialAttractive forceRepulsive CoreWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 6• Nuclear force keeps the nucleons within the nucleus. – What does this tell you about the nature of the nuclear force?⇒It must be attractive!!• However, scattering experiments with high energy revealed a repulsive core!!– Below a certain length scale, the nuclear force changes from attractive to repulsive.– What does this tell you?• Nucleons have substructure….• This repulsive feature is good, why?– If the nuclear force were attractive at all distances, the nucleus would collapse in on itself.Shape of the Nuclear PotentialWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 7Nuclear Potential w/ Coulomb Corrections Results in• Classically an incident proton with total energy E0cannot be closer than r=r0. Why?– For R<r<r0, V(r) >E0and KE<0 Physically impossible• What about a neutron?– Could penetrate into the nuclear center.• Low energy scattering experiments did not provide the exact shape of the potential but did give info on the range and height of the potential• The square-well shape provides a good phenomenological description of the nuclear force.Wednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 8• A square well nuclear potential provides the basis of quantum theory with discrete energy levels and corresponding bound state just like in atoms– Presence of nuclear quantum states have been confirmed through • Scattering experiments• Studies of the energies emitted in nuclear radiation• Studies of mirror nuclei and the scatterings of protons and neutrons demonstrate– Aside from the Coulomb effects, the forces between two neutrons, two protons or a proton and a neutron are the same • Nuclear force has nothing to do with electrical charge• Protons and neutrons behave the same under the nuclear force– Referred to as charge independence of nuclear force.Nuclear PotentialWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 9• Strong nuclear force is independent of the electric charge carried by nucleons– Concept of strong isotopic-spin symmetry.• proton and neutron are the two different iso-spin state of the same particle called nucleon– In other words,• If Coulomb effect were turned off, protons and neutrons would be indistinguishable in their nuclear interactions• Can you give another case just like this???– This is analogous to the indistinguishability of spin up and down states in the absence of a magnetic field!!• This is called Iso-spin symmetry!!! (predates quark model, no longer really used except in Nuclear classes!)Nuclear Potential – Iso-spin symmetryWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 10• EM force can be understood as a result of a photon exchange– Photon propagation is described by the Maxwell’s equation– Photons propagate at the speed of light. – What does this tell you about the mass of the photon?• Massless• Coulomb potential is• What does this tell you about the range of the Coulomb force?– Long range. Range of the Nuclear Force( )Vr∝1rMassless particle exchangeWednesday, Sept. 29, 2010 PHYS 3446, Fall 2010 Andrew Brandt 11• For massive particle exchanges, the potential takes the form– What is the
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