|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In [[nuclear physics]] and [[nuclear chemistry]], the '''nuclear shell model''' is a [[nuclear model|model of]] the [[atomic nucleus]] which uses the [[Pauli exclusion principle]] to describe the structure of the nucleus in terms of energy levels.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html Nuclear Shell Model]</ref> The first shell model was proposed by [[Dmitry Ivanenko]] (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably [[Eugene Paul Wigner]], [[Maria Goeppert-Mayer]] and [[J. Hans D. Jensen]], who shared the 1963 [[Nobel Prize in Physics]] for their contributions.
| | Dental care isn't easy, this needs to be an activity that you are currently engaging in.You should be diligent with your care to be able to enjoy a lifetime of healthy one. The following article below has some advice that many people have once had great tried and true advice for optimal dental hygiene.<br><br>Cavities can produce each time a tooth's enamel is weakened. Bacteria weakens your enamel and that leads to cavities. Be sure you view your dentist appointment every six months time to stop cavities. Your dentist may periodically x-ray your teeth this permits because of it.<br><br>If you're scared of the dentist, research local dentists to view what they have to offer. Take a look at reviews on the best dentists in your town.This allows you to feel safe throughout your visits.<br><br>Use a different make of toothpaste should you experience sensitivity. Before assuming it is just sensitive teeth, attempt to make a consultation to see your dentist. Your dentist will help you determine the cause of your teeth sensitivity.<br><br>You should make your toothbrush remain clean. After you are finished brushing, rinse it and allow it to air dry. Use it within a toothbrush holder when you finish brushing so you don't contaminate your toothbrush head. Don't keep your toothbrush in a closed container where bacteria can lead to the expansion of bacteria. Change your toothbrush regularly.<br><br>In addition, you are likely to need to floss your teeth regularly and make use of antiseptic mouthwash.Make the 3 element of this stuff.<br><br>Dental hygiene is a thing you need to stay up with, even should you not have any natural teeth. Brush your dentures just as you will your real teeth.<br><br>Your tongue is as essential as your oral health. To keep your tongue healthy and clean, a tongue scraper ought to be used on your dental routine. This may get excess bacteria that develops on the tongue.You should use your toothbrush should you don't have got a tongue scraper.<br><br>Don't ever take tooth pain lightly. Pain might be a while may mean which you have infection you need to take care of right away. Call your dentist to talk about the situation right away and set up a consultation.<br><br>You need to brush for 2 minutes.The greater time you may spend brushing, the cleaner they are, so spend time and do it properly. In the event you rush the task, you'll leave a lot behind and end up having cavities.<br><br>Whenever you buy toothpaste, ensure that you purchase one which has fluoride inside it. This will aid strengthen your teeth therefore they don't have several cavities or some other problems such as that. Strong teeth ultimately are healthy teeth.<br><br>Ask friends and relations when seeking a dentist. They are able to often fill you will be interested in learning patient treatment and measure of office professionalism.<br><br>Buy flossing pics therefore you to utilize or even to remember. These picks are only floss that's in the stick-like form. They can be convenient as their design allows you to just pull one out and commence flossing. Some think it's much easier to use these products to traditional floss. This really is can be useful for kids who may have a difficult time handling traditional dental floss.<br><br>Limit the level of carbonated beverages you drink.Acid can be a major ingredient in every cola drinks. This acid can discolor and discolors the enamel on your teeth. Drink using a straw.You must also brush soon after drinking and then rinse teeth with water.<br><br>Looking after your teeth is essential for many reasons. There is no method to turn back damage in the event you falter within your dental hygiene. This article has offered basic steps for excellent oral health. Start today to maintain your smile healthy.<br><br>If you have any inquiries pertaining to the place and how to use [http://www.wiki.psychonaut.cz/wiki/index.php?title=Dental_Treatments_Advice_That_Everybody_Can_Use http://www.wiki.psychonaut.cz/], you can speak to us at our web page. |
| | |
| The shell model is partly analogous to the [[Electron configuration|atomic shell model]] which describes the arrangement of [[electron]]s in an atom, in that a filled shell results in greater stability. When adding [[nucleon]]s ([[proton]]s or [[neutron]]s) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain [[Magic number (physics)|magic number]]s of nucleons: 2, 8, 20, 28, 50, 82, 126 which are more tightly bound than the next higher number, is the origin of the shell model.
| |
| | |
| The shells for protons and for neutrons are independent of each other. Therefore, one can have "magic nuclei" where one nucleon type or the other is at a magic number, and "[[Magic number (physics)#Double magic|doubly magic nuclei]]", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons, playing a role in the search of the so-called [[island of stability]]. There have been found some semimagic numbers, notably Z=40 giving nuclear shell filling for the various elements; 16 may also be a magic number.<ref>{{cite journal|last1=Ozawa|first1=A.|last2=Kobayashi|first2=T.|last3=Suzuki|first3=T.|last4=Yoshida|first4=K.|last5=Tanihata|first5=I.|title=New Magic Number, N=16, near the Neutron Drip Line|journal=Physical Review Letters|volume=84|issue=24|pages=5493|year=2000|pmid=10990977|doi=10.1103/PhysRevLett.84.5493|bibcode=2000PhRvL..84.5493O}}</ref>
| |
| | |
| In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the [[square well]] and the [[harmonic oscillator]]. To this potential a spin orbit term is added. Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling, named the [[Nilsson Term]], must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied.
| |
| <!-- Image with unknown copyright status removed: [[Image:Shellmod.gif]] -->
| |
| | |
| Nevertheless, the magic numbers of nucleons, as well as other properties, can be arrived at by approximating the model with a [[Quantum harmonic oscillator#Example: 3D isotropic harmonic oscillator|three-dimensional harmonic oscillator]] plus a [[spin-orbit interaction]]. A more realistic but also complicated potential is known as [[Woods Saxon potential]].
| |
| | |
| [[Igal Talmi]] developed a method to obtain the information from experimental data and use it to calculate and predict energies which have not been measured. This method has been successfully used by many nuclear physicists and has led to deeper understanding of nuclear structure. The theory which gives a good description of these properties was developed. This description turned out to furnish the shell model basis of the elegant and successful [[Interacting boson model]].
| |
| | |
| ==Deformed harmonic oscillator approximated model==
| |
| Consider a [[Quantum harmonic oscillator#Example: 3D isotropic harmonic oscillator|three-dimensional harmonic oscillator]]. This would give, for example, in the first two levels (''"l"'' is angular momentum)
| |
| {| class="wikitable"
| |
| !width=50| level ''n''
| |
| !width=50| ''l''
| |
| !width=50| ''m<sub>l</sub>''
| |
| !width=50| m<sub>s</sub>
| |
| |-align=right
| |
| | rowspan=2|1 || rowspan=2| 0 || rowspan=2| 0 || {{frac|2}}
| |
| |-align=right
| |
| | −{{frac|2}}
| |
| |-align=right
| |
| | rowspan=6|1 || rowspan=6|1 || rowspan=2|1 || {{frac|2}}
| |
| |-align=right
| |
| | −{{frac|2}}
| |
| |-align=right
| |
| | rowspan=2|0 || {{frac|2}}
| |
| |-align=right
| |
| | −{{frac|2}}
| |
| |-align=right
| |
| | rowspan=2|−1 || {{frac|2}}
| |
| |-align=right
| |
| | −{{frac|2}}
| |
| |}
| |
| | |
| We can imagine ourselves building a nucleus by adding protons and neutrons. These will always fill the lowest available level. Thus the first two protons fill level zero, the next six protons fill level one, and so on. As with electrons in the [[periodic table]], protons in the outermost shell will be relatively loosely bound to the nucleus if there are only few protons in that shell, because they are farthest from the center of the nucleus. Therefore nuclei which have a full outer proton shell will have a higher [[binding energy]] than other nuclei with a similar total number of protons. All this is true for neutrons as well.
| |
| | |
| This means that the magic numbers are expected to be those in which all occupied shells are full. We see that for the first two numbers we get 2 (level 0 full) and 8 (levels 0 and 1 full), in accord with experiment. However the full set of magic numbers does not turn out correctly. These can be computed as follows:
| |
| | |
| :In a [[Quantum harmonic oscillator#Example: 3D isotropic harmonic oscillator|three-dimensional harmonic oscillator]] the total [[degenerate energy level|degeneracy]] at level n is <math>{(n+1)(n+2)\over 2}</math>. Due to the [[Spin (physics)|spin]], the degeneracy is doubled and is <math>(n+1)(n+2)</math>.
| |
| :Thus the magic numbers would be
| |
| :<math>{\sum_{n=0}}^k (n+1)(n+2) = {(k+1)(k+2)(k+3)\over 3}</math>
| |
| :for all integer k. This gives the following magic numbers: 2,8,20,40,70,112..., which agree with experiment only in the first three entries. These numbers are twice the tetrahedral numbers (1,4,10,20,35,56...) from the [[Pascal's triangle|Pascal Triangle]].
| |
| | |
| In particular, the first six shells are:
| |
| * level 0: 2 states (''l'' = 0) = 2.
| |
| * level 1: 6 states (''l'' = 1) = 6.
| |
| * level 2: 2 states (''l'' = 0) + 10 states (''l'' = 2) = 12.
| |
| * level 3: 6 states (''l'' = 1) + 14 states (''l'' = 3) = 20.
| |
| * level 4: 2 states (''l'' = 0) + 10 states (''l'' = 2) + 18 states (''l'' = 4) = 30.
| |
| * level 5: 6 states (''l'' = 1) + 14 states (''l'' = 3) + 22 states (''l'' = 5) = 42.
| |
| where for every ''l'' there are 2''l''+1 different values of ''m<sub>l</sub>'' and 2 values of ''m<sub>s</sub>'', giving a total of 4''l''+2 states for every specific level. | |
| | |
| These numbers are twice the values of triangular numbers from the Pascal Triangle: 1,3,6,10,15,21....
| |
| | |
| ===Including a spin-orbit interaction===
| |
| We next include a [[spin-orbit interaction]]. First we have to describe the system by the [[Quantum number#Quantum numbers with spin-orbit interaction|quantum numbers]] ''j'', ''m<sub>j</sub>'' and [[Parity (physics)|parity]] instead of ''l'', ''m<sub>l</sub>'' and ''m<sub>s</sub>'', as in the [[Hydrogen-like atom#Including spin-orbit interaction|Hydrogen-like atom]]. Since every even level includes only even values of ''l'', it includes only states of even (positive) parity; Similarly every odd level includes only states of odd (negative) parity. Thus we can ignore parity in counting states. The first six shells, described by the new quantum numbers, are
| |
| * level 0 (''n''=0): 2 states (''j'' = {{frac|2}}). Even parity.
| |
| * level 1 (''n''=1): 2 states (''j'' = {{frac|2}}) + 4 states (''j'' = {{frac|3|2}}) = 6. Odd parity.
| |
| * level 2 (''n''=2): 2 states (''j'' = {{frac|2}}) + 4 states (''j'' = {{frac|3|2}}) + 6 states (''j'' = {{frac|5|2}}) = 12. Even parity.
| |
| * level 3 (''n''=3): 2 states (''j'' = {{frac|2}}) + 4 states (''j'' = {{frac|3|2}}) + 6 states (''j'' = {{frac|5|2}}) + 8 states (''j'' = {{frac|7|2}}) = 20. Odd parity.
| |
| * level 4 (''n''=4): 2 states (''j'' = {{frac|2}}) + 4 states (''j'' = {{frac|3|2}}) + 6 states (''j'' = {{frac|5|2}}) + 8 states (''j'' = {{frac|7|2}}) + 10 states (''j'' = {{frac|9|2}}) = 30. Even parity.
| |
| * level 5 (''n''=5): 2 states (''j'' = {{frac|2}}) + 4 states (''j'' = {{frac|3|2}}) + 6 states (''j'' = {{frac|5|2}}) + 8 states (''j'' = {{frac|7|2}}) + 10 states (''j'' = {{frac|9|2}}) + 12 states (''j'' = {{frac|11|2}}) = 42. Odd parity.
| |
| where for every ''j'' there are {{gaps|2''j''|+|1}} different states from different values of ''m<sub>j</sub>''.
| |
| | |
| Due to the spin-orbit interaction the energies of states of the same level but with different ''j'' will no longer be identical. This is because in the original quantum numbers, when <math>\scriptstyle \vec{s}</math> is parallel to <math>\scriptstyle \vec{l}</math>, the interaction energy is positive; and in this case ''j'' = ''l'' + ''s'' = ''l'' + {{frac|2}}. When <math>\scriptstyle \vec{s}</math> is anti-parallel to <math>\scriptstyle \vec{l}</math> (i.e. aligned oppositely), the interaction energy is negative, and in this case {{gaps|''j''|{{=}}|''l''|−|''s''|{{=}}|''l''|−|{{frac|2}}}}. Furthermore, the strength of the interaction is roughly proportional to ''l''.
| |
| | |
| For example, consider the states at level 4:
| |
| * The 10 states with ''j'' = {{frac|9|2}} come from ''l'' = 4 and ''s'' parallel to ''l''. Thus they have a positive spin-orbit interaction energy.
| |
| * The 8 states with ''j'' = {{frac|7|2}} came from ''l'' = 4 and ''s'' anti-parallel to ''l''. Thus they have a negative spin-orbit interaction energy.
| |
| * The 6 states with ''j'' = {{frac|5|2}} came from ''l'' = 2 and ''s'' parallel to ''l''. Thus they have a positive spin-orbit interaction energy. However its magnitude is half compared to the states with ''j'' = {{frac|9|2}}.
| |
| * The 4 states with ''j'' = {{frac|3|2}} came from ''l'' = 2 and ''s'' anti-parallel to ''l''. Thus they have a negative spin-orbit interaction energy. However its magnitude is half compared to the states with ''j'' = {{frac|7|2}}.
| |
| * The 2 states with ''j'' = {{frac|2}} came from ''l'' = 0 and thus have zero spin-orbit interaction energy.
| |
| | |
| ===Deforming the potential===
| |
| The [[harmonic oscillator]] potential <math>V(r) = \mu \omega^2 r^2 /2</math> grows infinitely as the distance from the center ''r'' goes to infinity. A more realistic potential, such as [[Woods Saxon potential]], would approach a constant at this limit. One main consequence is that the average radius of nucleons' orbits would be larger in a realistic potential; This leads to a reduced term <math>\scriptstyle \hbar^2 l(l+1)/ 2m r^2</math> in the [[Laplace operator]] of the [[Hamiltonian (quantum mechanics)|Hamiltonian]]. Another main difference is that orbits with high average radii, such as those with high ''n'' or high ''l'', will have a lower energy than in a harmonic oscillator potential. Both effects lead to a reduction in the energy levels of high ''l'' orbits.
| |
| | |
| ===Predicted magic numbers===
| |
| [[Image:Shells.png|thumb|right|Low-lying energy levels in a single-particle shell model with an oscillator potential (with a small negative ''l<sup>2</sup>'' term) without spin-orbit (left) and with spin-orbit (right) interaction. The number to the right of a level indicates its degeneracy, (''2j+1''). The boxed integers indicate the magic numbers.]]
| |
| | |
| Together with the spin-orbit interaction, and for appropriate magnitudes of both effects, one is led to the following qualitative picture: At all levels, the highest ''j'' states have their energies shifted downwards, especially for high ''n'' (where the highest ''j'' is high). This is both due to the negative spin-orbit interaction energy and to the reduction in energy resulting from deforming the potential to a more realistic one. The second-to-highest ''j'' states, on the contrary, have their energy shifted up by the first effect and down by the second effect, leading to a small overall shift. The shifts in the energy of the highest ''j'' states can thus bring the energy of states of one level to be closer to the energy of states of a lower level. The "shells" of the shell model are then no longer identical to the levels denoted by ''n'', and the magic numbers are changed.
| |
| | |
| We may then suppose that the highest ''j'' states for ''n'' = 3 have an intermediate energy between the average energies of ''n'' = 2 and ''n'' = 3, and suppose that the highest ''j'' states for larger ''n'' (at least up to ''n'' = 7) have an energy closer to the average energy of {{gaps|''n''|−|1}}. Then we get the following shells (see the figure)
| |
| | |
| * 1st shell:  2 states (''n'' = 0, ''j'' = {{frac|2}}).
| |
| * 2nd shell:  6 states (''n'' = 1, ''j'' = {{frac|2}} or {{frac|3|2}}).
| |
| * 3rd shell: 12 states (''n'' = 2, ''j'' = {{frac|2}}, {{frac|3|2}} or {{frac|5|2}}).
| |
| * 4th shell:  8 states (''n'' = 3, ''j'' = {{frac|7|2}}).
| |
| * 5th shell: 22 states (''n'' = 3, ''j'' = {{frac|2}}, {{frac|3|2}} or {{frac|5|2}}; ''n'' = 4, ''j'' = {{frac|9|2}}).
| |
| * 6th shell: 32 states (''n'' = 4, ''j'' = {{frac|2}}, {{frac|3|2}}, {{frac|5|2}} or {{frac|7|2}}; ''n'' = 5, ''j'' = {{frac|11|2}}).
| |
| * 7th shell: 44 states (''n'' = 5, ''j'' = {{frac|2}}, {{frac|3|2}}, {{frac|5|2}}, {{frac|7|2}} or {{frac|9|2}}; ''n'' = 6, ''j'' = {{frac|13|2}}).
| |
| * 8th shell: 58 states (''n'' = 6, ''j'' = {{frac|2}}, {{frac|3|2}}, {{frac|5|2}}, {{frac|7|2}}, {{frac|9|2}} or {{frac|11|2}}; ''n'' = 7, ''j'' = {{frac|15|2}}).
| |
| and so on.
| |
| | |
| The magic numbers are then
| |
| | |
| *   2
| |
| *   {{gaps|8|{{=}}|2|+|6}}
| |
| *  {{gaps|20|{{=}}|2|+|6|+|12}}
| |
| *  {{gaps|28|{{=}}|2|+|6|+|12|+|8}}
| |
| *  {{gaps|50|{{=}}|2|+|6|+|12|+|8|+|22}}
| |
| *  {{gaps|82|{{=}}|2|+|6|+|12|+|8|+|22|+|32}}
| |
| * {{gaps|126|{{=}}|2|+|6|+|12|+|8|+|22|+|32|+|44}}
| |
| * {{gaps|184|{{=}}|2|+|6|+|12|+|8|+|22|+|32|+|44|+|58}}
| |
| | |
| and so on. This gives all the observed magic numbers, and also predicts a new one (the so-called ''[[island of stability]]'') at the value of 184 (for protons, the magic number 126 has not been observed yet, and more complicated theoretical considerations predict the magic number to be 114 instead).
| |
| | |
| Another way to predict magic (and semi-magic) numbers is by laying out the idealized filling order (with spin-orbit splitting but energy levels not overlapping). For consistency s is split into j = 1⁄2 and j = -1⁄2 components with 2 and 0 members respectively. Taking leftmost and rightmost total counts within sequences marked bounded by / here gives the magic and semi-magic numbers.
| |
| | |
| * s(2,0)/p(4,2)> 2,2/6,8, so (semi)magic numbers 2,2/6,8
| |
| * d(6,4):s(2,0)/f(8,6):p(4,2)> 14,18:20,20/28,34:38,40, so 14,20/28,40
| |
| * g(10,8):d(6,4):s(2,0)/h(12,10):f(8,6):p(4,2)> 50,58,64,68,70,70/82,92,100,106,110,112, so 50,70/82,112
| |
| * i(14,12):g(10,8):d(6,4):s(2,0)/j(16,14):h(12,10):f(8,6):p(4,2)> 126,138,148,156,162,166,168,168/184,198,210,220,228,234,238,240, so 126,168/184,240
| |
| | |
| The rightmost predicted magic numbers of each pair within the quartets bisected by / are double tetrahedral numbers from the Pascal Triangle: 2,8,20,40,70,112,168,240 are 2x 1,4,10,20,35,56,84,120..., and the leftmost members of the pairs differ from the rightmost by double triangular numbers: 2-2=0, 8-6=2, 20-14=6, 40-28=12, 70-50=20, 112-82=30, 168-126=42, 240-184=56, where 0,2,6,12,20,30,42,56... are 2x 0,1,3,6,10,15,21,28....
| |
| | |
| ===Other properties of nuclei===
| |
| This model also predicts or explains with some success other properties of nuclei, in particular [[Spin (physics)|spin]] and [[Parity (physics)|parity]] of nuclei [[ground state]]s, and to some extent their [[excited state]]s as well. Take {{chem|link=Isotopes of oxygen|17|8|O}} as an example — its nucleus has eight protons filling the three first proton 'shells', eight neutrons filling the three first neutron 'shells', and one extra neutron. All protons in a complete proton shell have total [[angular momentum]] zero, since their angular momenta cancel each other; The same is true for neutrons. All protons in the same level (''n'') have the same parity (either +1 or −1), and since the parity of a pair of particles is the product of their parities, an even number of protons from the same level (''n'') will have +1 parity. Thus the total angular momentum of the eight protons and the first eight neutrons is zero, and their total parity is +1. This means that the spin (i.e. angular momentum) of the nucleus, as well as its parity, are fully determined by that of the ninth neutron. This one is in the first (i.e. lowest energy) state of the 4th shell, which is a d-shell (''l'' = 2), and since <math>p= (-1)^l</math>, this gives the nucleus an overall parity of +1. This 4th d-shell has a ''j'' = {{frac|5|2}}, thus the nucleus of {{chem|17|8|O}} is expected to have positive parity and total angular momentum {{frac|5|2}}, which indeed it has. | |
| | |
| The rules for the ordering of the nucleus shells are similar to [[List of Hund's rules|Hund's Rules]] of the atomic shells, however, unlike its use in atomic physics the completion of a shell is not signified by reaching the next ''n'', as such the shell model cannot accurately predict the order of excited nuclei states, though it is very successful in predicting the ground states. The order of the first few terms are listed as follows: 1s, 1p{{frac|3|2}}, 1p{{frac|1|2}}, 1d{{frac|5|2}}, 2s, 1d{{frac|3|2}}... For further clarification on the notation refer to the article on the Russell-Saunders [[term symbol]].
| |
| | |
| For nuclei farther from the [[Magic number (physics)|magic numbers]] one must add the assumption that due to the relation between the [[strong nuclear force]] and angular momentum, [[proton]]s or [[neutron]]s with the same ''n'' tend to form pairs of opposite angular momenta. Therefore a nucleus with an even number of protons and an even number of neutrons has 0 spin and positive parity. A nucleus with an even number of protons and an odd number of neutrons (or vice versa) has the parity of the last neutron (or proton), and the spin equal to the total angular momentum of this neutron (or proton). By "last" we mean the properties coming from the highest energy level.
| |
| | |
| In the case of a nucleus with an odd number of protons and an odd number of neutrons, one must consider the total angular momentum and parity of both the last neutron and the last proton. The nucleus parity will be a product of theirs, while the nucleus spin will be one of the possible results of the [[Angular momentum#Addition of quantized angular momenta|sum]] of their angular momenta (with other possible results being excited states of the nucleus).
| |
| | |
| The ordering of angular momentum levels within each shell is according to the principles described above - due to spin-orbit interaction, with high angular momentum states having their energies shifted downwards due to the deformation of the potential (i.e. moving from a harmonic oscillator potential to a more realistic one). For nucleon pairs, however, it is often energetically favorable to be at high angular momentum, even if its energy level for a single nucleon would be higher. This is due to the relation between angular momentum and the [[strong nuclear force]].
| |
| | |
| [[Nuclear magnetic moment]] is partly predicted by this simple version of the shell model. The magnetic moment is calculated through ''j'', ''l'' and ''s'' of the "last" nucleon, but nuclei are not in states of well defined ''l'' and ''s''. Furthermore, for [[odd-odd nuclei]], one has to consider the two "last" nucleons, as in [[Deuterium#Magnetic and electric multipoles|deuterium]]. Therefore one gets several possible answers for the nuclear magnetic moment, one for each possible combined ''l'' and ''s'' state, and the real state of the nucleus is a [[Superposition principle|superposition]] of them. Thus the real (measured) nuclear magnetic moment is somewhere in between the possible answers.
| |
| | |
| The [[electric dipole]] of a nucleus is always zero, because its [[ground state]] has a definite parity, so its matter density (<math>\psi^2</math>, where <math>\psi</math> is the [[wavefunction]]) is always invariant under parity. This is usually the situations with the [[Dipole#Atomic dipoles|atomic electric dipole]] as well.
| |
| | |
| Higher electric and magnetic [[multipole moments]] cannot be predicted by this simple version of the shell model, for the reasons similar to those in the case of the [[Deuterium#Magnetic and electric multipoles|deuterium]].
| |
| | |
| ==Alpha particle model==
| |
| A model derived from the nuclear shell model is the alpha particle model developed by [[Henry Margenau]], [[Edward Teller]], J. K. Pering, [[T.H. Skyrme]].
| |
| | |
| ==See also==
| |
| * [[Interacting boson model]]
| |
| * [[Liquid drop model]]
| |
| * [[Nuclear structure]]
| |
| * [[Isomeric shift]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==Books==
| |
| * {{cite book|url=http://www.amazon.com/Nuclear-Shell-Theory-Dover-Editions/dp/048643933X |title=Nuclear Shell Theory|first1=Igal |last1=Talmi |first2=A. |last2=de-Shalit |year=1963|publisher= Academic Press, (reprinted by Dover Publications)|isbn=0-486-43933-X}}
| |
| * {{cite book|url=http://www.amazon.co.uk/Simple-Models-Complex-Nuclei-Contemporary/dp/3718605503|title=Simple Models of Complex Nuclei: The Shell Model and the Interacting Boson Model|first=Igal |last=Talmi |year=1993|publisher= Harwood Academic Publishers|isbn=3-7186-0551-1}}
| |
| | |
| ==Recent Lecture==
| |
| * {{cite video|url=http://ribf.riken.jp/Lecture/Talmi-24Nov2010/|title=On single nucleon wave functions |people= Igal Talmi| date=Nov 24, 2010|location= RIKEN Nishina Center}}
| |
| Internet streaming broadcasting both on WM and QT at (at 64 kbit/s, 256 kbit/s, 1 Mbit/s ) and DVD ISO (NTSC and PAL) delivery are now available at RIKEN Nishina Center.
| |
| | |
| {{DEFAULTSORT:Nuclear Shell Model}}
| |
| [[Category:Nuclear physics]]
| |