Random walk model of consumption: Difference between revisions

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In lots of instances, folks merely forgot they hadthese items.<br><br>My [http://sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=%5B%5Biframe+%2F%2Fwww.youtube.com%2Fembed%2FNt9fxWq5qg0+height%3D%22360%22+width%3D%22640%22%5D%5DDown+behind+enemy+traces%3F+Left+to+fend+for+your+self%3F++Should+you+have+just+about+any+%5Bhttp%3A%2F%2Fwww.Twitpic.com%2Ftag%2Fconcerns+concerns%5D+concerning+where+and+the+best+way+to+make+use+of+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fgerber-knives-review%2F+Thebestpocketknifereviews.com%5D%2C+you+can+call+us+with+the+site.+These+are+the+%5Bhttp%3A%2F%2FSearch.un.org%2Fsearch%3Fie%3Dutf8%26site%3Dun_org%26output%3Dxml_no_dtd%26client%3DUN_Website_en%26num%3D10%26lr%3Dlang_en%26proxystylesheet%3DUN_Website_en%26oe%3Dutf8%26q%3Dscenarios%26Submit%3DGo+scenarios%5D+that+%5Bhttp%3A%2F%2FBrowse.Deviantart.com%2F%3Fqh%3D%26section%3D%26global%3D1%26q%3Dimpressed+impressed%5D+the+LMF+II.+Former+army+man%2C+Jeff+Freeman+led+the+cost+to+engineer+this+fearless+new+10%22+survival+knife.+And+we+field-tested+with+the+troops.%0D%0A%0D%0ANow+lets+get+again+to+business+and+assessment+the+Paraframe+I.+The+Paraframe+I+has+eight+totally+different+knives+within+the+sequence.carry+the+serrated+for+those+further+robust+slicing+jobs.+The+Paraframe+I+relies+on+a+minimal+body+lock+design.+It%27s+splendidly+simple%2C+open+body%28skeleton%29+knife+with+a+serrated+locking+blade+that+is+super+light-weight%2C+it+cleans+simply+and+opens+effortlessly.+The+Paraframe+is+constructed+with+a+easy+chrome+steel+handle+and+a+pocket+clip+to+secure+the+blade+to+your+pocket.+The+knife+has+an+general+size+of+seven.01+inches+with+a+blade+size+of+three.01+inches.+The+Paraframe+is+a+great+on+a+regular+basis+folder.%0D%0A%0D%0AIf+you+happen+to+want+an+enormous%2C+beefy+combat+knife+that+may+lower+and+slice+with+the+best+of+them%2C+the+Gerber+DMF+is+one+I+like+to+recommend.+After+utilizing+the+knife+for+30+days%2C+I%27ve+come+to+the+conclusion+that+it+is+a+well+made%2C+sturdy+knife+that+may+take+heavy+abuse.+With+an+S30V+blade%2C+G-10+handle+scales+that+give+your+hand+plenty+of+grip%2C+and+a+no+nonsense+attitude%2C+the+DMF+will+get+an+A+grade.+The+Gerber+Steadfast+is+sold+complete+with+a+Cordura+sheath+that+includes+a+MOLLE+attachment+system+on+the+again+in+addition+to+a+large+belt+loop%2C+a+handy+and+a+leg+strap+with+quick+launch+buckle+is+also+supplied.+The+black+is+lined+with+a+plastic+protecting+liner+that+keeps+the+sheath+in+shape+and+prevents+the+sting+from+damaging+it.+Opening+up+a+can+with+the+knife%0D%0A%0D%0AErgonomics+for+this+folder+are+outstanding%21+The+deal+with+is+coated+with+a+grippy+rubbery+material+that%2C+together+with+the+striped+pattern+within+the+handle%2C+jimping%2C+and+a+deep+finger+choile%2C+provide+the+consumer+a+secure+grip+regardless+of+how+slippery+the+situations+get.+Throughout+the+handle+is+a+lockback+mechanism+supporting+the+folding+blade.+This+design+is+usually+stronger+than+a+linerlock+mechanism%2C+making+this+Gerber+Bear+Grylls+product+one+of+the+better+decisions+for+a+survival+folder.%0D%0A%0D%0AThe+sheath+is+reversible+and+allows+you+to+carry+the+knife+with+the+tip+pointing+up%2C+down%2C+or+horizontally.+The+sheath+additionally+has+a+belt+loop+that+is+adjustable+and+may+be+eliminated+and+laced+to+tactical+and+other+gear.+The+sheath+has+good+retention+and+seats+with+an+audible+click%2C+however+does+not+require+the+push+of+a+button+to+draw+the+knife+%28Massive+plus+IMHO%29.+Chances+are+you%27ll+check+your+order+status+by+clicking+the+Order+Standing+tab+in+the+LA+Police+Gear+Customer+Service+Center.+Please+be+sure+to+enter+the+zip+code+you+entered+in+your+billing+address.+You+probably+have+registered+for+an+account+with+LA+Police+Gear%2C+you+possibly+can+view+your+entire+order+history+by+clicking+My+Account.+Can+I+buy+from+LA+Police+Gear+if+I%27m+not+within+the+navy%2C+legislation+enforcement%2C+and+many+others.%3F%0D%0A%0D%0AThis+knife+is+a+good+software+to+keep+in+your+tool+field+or+tool+belt.+It+is+a+good+working+knife+since+it+might+probably+assist+with+the+tools+like+cleaning+off+the+underside+of+lawn+mower+deck.+Gerber+has+made+it+a+degree+to+use+scallop+serrations+since+it%27s+not+onerous+to+re+sharpen+the+knife.+For+those+who+dislike+difficult+sharpening+procedures+this+is+the+right+knife+that+permits+its+proprietor+to+make+use+of+it+over+and+over+again.+This+knife+has+a+slim+deal+with+which+has+two+lashing+holes+in+it+when+there%27s+a+have+to+affix+a+spear.%0D%0A%0D%0ANot+all+knife+brands+would+not+offer+a+special+provide+for+their+customers.+Thankfully%2C+if+you+happen+to%27re+prepared+to+purchase+a+gerber+knife+then+we+now+have+a+excellent+news+for+you.+All+the+gerber+knives+are+backed+by+full+lifetime+guarantee+%28+25+years+outside+of+the+country+%29.+This+give+a+guarantee+that+the+knife+will+final+for+lifetime.+This+is+likely+one+of+the+very+unique+guarantee+that+no+other+firm+would+possibly+offer.+The+Silver+Trident+is+the+most+advanced+Gerber+Knife+you+Blade+ownCould+Gerber%27s+superior+recognition+for+high-quality+makes+this+Gerber%27s+many+innovative+knife+and+one+that+may+actually+final+you+generations.+The+Gerber+LMF+II+survival+knife+has+a+really+wide+blade+that%27s+3%2F16s+of+an+inch+assume%2C+4.eighty+four+inches+lengthy.+Stainless+Steel+Mounted+Blade+Searching+Knife+made+by+Gerber%0D%0A%0D%0AThe+Kershaw+1780CB+Cutting+knife%2C+known+additionally+because+the+Kershaw+Rake%2C+is+a+composite+folding+knife+that+features+wear-resistant+D2+steel+on+its+cutting+edge+and+Sandvik+14C28N+metal+on+the+spine.+This+pretty+priced+knife+has+high+opinions+and+ratings+on-line.+Amazon+customers+were+impressed+with+many+options+of+the+Fast+Draw.+One+buyer+wrote+that+it+holds+the+edge+effectively+and+sharpens+fairly+easily.+One+other+wrote+that+the+design+was+very+lightweight+and+compact%2C+and+that+the+deal+with+matches+snug+in+your+hand.+Others+famous+that+the+pocket+clip+was+a+great+function.+General%2C+Amazon+reviews+wrote+that+at+lower+than+%2430%2C+the+Quick+Draw+was+a+stable+possibility+in+the+event+you%27re+searching+for+an+everyday+carry+pocket+knife.+Gerber+brand+on+machete%2Fsaw+combo+Priorities+of+survival+information&create=Create largest] and probably solely drawback with the Ruger Standard Model came when stripping it down for cleaning. There's a steel lever in the rear of the pistol grip that unfolds like a pocket knife, permitting the barreled receiver to be separated from the body. In this situation, the bolt might be faraway from the receiver and the gun cleaned thoroughly. What I did not discover on the time was that the tiny rebound spring popped misplaced on the bolt when I reassembled the gun. The bolt locked solidly into place and I couldn't get the gun back aside.<br><br>Although the opinions are mainly positive, a number of red flags have been unfurled by clients. The commonest is within the preliminary that's in part 1 of the eating regimen. For the reason that carb intake is sort of nil in phase 1, it may possibly result in a basic feeling of fatigue. However, this downside is taken care of sooner or later of the weight loss program itself. Few clients additionally report minor issues or complaints like constipation. Nevertheless, such reports are rare. Additionally in case of such problems, the official website has contact details of pros and medical doctors that offer one-on-one assistance that can enable you to sort out the issue you are dealing with.<br><br>While I recognize that lots of people use knives for self protection, hence its mention on this article, I don’t typically suggest a knife as a self protection tool in untrained hands. Because of this, I can't be recommending any knives particular to this use on this article. For a self defense advice, I counsel pepper spray, as it will possibly shortly and non-lethally disable a number of attackers from a distance and is tough to turn and use in opposition to you. I'll yield self protection knife suggestions to people who have the suitable coaching on this area. A Fast Phrase About Features<br><br>There are friction factors on the highest and butt of the handle scales, that significantly assist in getting a secure grip on the knife in many different types of knife combating holds. And, there's a very slight upward angle on the entrance prime of the deal with scales for proper [http://Thebestpocketknifereviews.com/gerber-knives-review/ http://Thebestpocketknifereviews.com/Gerber-knives-review/] thumb placement in the fencing grip. On the bottom front of the handle scales, there are also friction points for [http://Esmikorea.ezconn.net/xe/?document_srl=80710 correct placement] of your index finger in the fencing grip. Closed size of the Entourage is four.70-inches and opened it's 8.44-inches and it weighs-in at 4.50-ounces-not too heavy and not too light.<br><br>Although Bowie knives are quite expensive paying an [http://Www.Vendomaquinas.Com.br/author/elswadling/ enormous] amount will not be needed when you recognize the value ranges acceptable for an authentic Bowie knife. Before you purchase a Bowie knife , just be sure you have compared costs extensively to get the very best deal. Bowie knives are common collectors' items and are sometimes positioned on the rare category particularly those which might be recognized to have been made by the unique makers prior to now. Some companies which might be identified to make Bowie knives are Bronks Knifework, JP Miller, Al Warren Customized Knife, Steve Mullin, Jim Ferguson, JP Holmes Customized, Knife Werks and extra.<br><br>This describes a knife carried by somebody who is distant from civilization that MUST depend on their knife as a life line. Reliability and robustness are of paramount importance. The requirements for this knife are probably the most stringent, far more so than these of an on a regular basis carry or light duty knife. A survival folding knife should only be used as a supplement to a survival mounted [http://www.thebestpocketknifereviews.com/gerber-knives-review/ Gerber Knives review] blade. There are one million uses for a pocket knife. Although they all involve slicing, as that is just about what a knife does, you can be surprised to understand how handy a pocket knife can turn out to be in common everyday conditions.
 
[[File:NuclideMap C-F.png|thumb|right|388px|[[Chart of nuclides]] for [[carbon]] to [[fluorine]]. [[Decay mode]]s:
<BR><BR>
{{legend|#ff9472|[[proton emission]]}}
{{legend|#e78cc7|[[positron emission]] or [[electron capture]]}}
{{legend|#000000|[[stable isotope]]}}
{{legend|#63c5de|[[beta decay]]}}
{{legend|#9b7bbc|[[neutron emission]]}}]]
 
In [[nuclear physics]], the boundaries for nuclear particle-stability are conceptualized as '''drip lines'''. The nuclear landscape is understood by plotting boxes, each of which represents a unique nuclear species, on a graph with the number of neutrons increasing on the [[abscissa]] (X axis) and number of protons increasing along the [[ordinate]] (Y axis), which is commonly referred to as the [[Chart of nuclides|table of nuclides]], being to [[nuclear physics]] what the more commonly known [[periodic table of the elements]] is to [[chemistry]].
 
However, an arbitrary combination of [[protons]] and [[neutrons]] does not necessarily yield a stable [[atomic nucleus|nucleus]], and ultimately when continuing to add more of the same type of [[nucleon]]s to a given nucleus, the newly formed nucleus will essentially undergo immediate decay where a nucleon of the same [[isospin|isospin quantum number]] (proton or neutron) is emitted; colloquially the nucleon has 'leaked' or 'dripped' out of the target nucleus, hence giving rise to the term "drip line". The nucleons drip out of such unstable nuclei for the same reason that water drips from a leaking faucet: the droplet, or nucleon in this case, sees a lower potential which is great enough to overcome surface tension in the case of water droplets, and the [[strong nuclear force]] in the case of [[proton emission]] or [[alpha decay]]. Because nucleons are [[Quantization (physics)|quantized]], only [[Integer|integer values]] are plotted on the table of isotopes; this indicates that the drip line is not [[linear]] but instead looks like a [[step function]] up close.
 
Drip lines are defined for protons, neutrons, and alpha particles, and these all play important roles in [[nuclear astrophysics]]. The nucleon (proton or neutron) drip lines are the extreme of proton-to-neutron (p:n) ratio: at p:n ratios at or beyond the driplines, no stable nuclei can exist.  
 
==General description==
Nuclear existence on the neutron-rich side of stability is limited by the neutron drip line, and on the proton-rich side stability is limited by the proton drip line. When the material has a reasonable balance of protons and neutrons, the total nuclear mass is limited by alpha decay, or the alpha drip line, which connects the proton and neutron drip lines, but is somewhat more confusing to visualize as it also branches down through the center of the chart. These limits exist because of particle decay, whereby an exothermic nuclear transition can occur by the emission of one or more nucleons (not to be confused with [[particle decay]] in [[particle physics]]).
 
While the concept of nuclear drip lines is very simple in principle because naturally occurring isotopes on Earth do not undergo proton or neutron emission, and to the complexity of the alpha drip line, the terms are not introduced in some undergraduate textbooks on nuclear physics.  The idea may become more commonplace with the advent of [[radioactive]] [[ion beam]] accelerators in the late 1980s, which are allowing nuclear physicists to readily probe the limits of nuclear stability. To understand the concept, one only needs to apply the principle of conservation of energy to [[Binding energy|nuclear binding energy]].
 
===Allowed transitions===
When considering whether a specific nuclear transmutation, a reaction or a decay, is energetically allowed, one only needs to sum the masses of the initial nucleus/nuclei and subtract from that value the sum of the masses of the out-going particles. If the result, or [[Q value (nuclear science)|Q-value]], is positive, then the transmutation is allowed, or exothermic because it releases energy, and if the Q-value is negative, then it is endothermic because at least that much energy must be added to the system before the transmutation may proceed. For example, if one wishes to ask if <sup>12</sup>C, the most common isotope of carbon, can undergo proton emission to <sup>11</sup>B, one finds that about 16 MeV must be added to the system for this process to be allowed. While Q-values can be used to describe any nuclear transmutations, for particle decay, the quantity S, or the particle separation energy, is also used, and it is equivalent to the negative of the Q-value; in other words, the proton separation energy S<sub>p</sub> indicates how much energy should be added to a given nucleus to remove a single proton. Thus, the particle drip lines are defined as the boundaries where the particle separation energy is less than or equal to zero, which is when spontaneous emission of that particle is energetically allowed.
 
==Nuclei near the drip lines are uncommon on Earth==
Of the three types of naturally occurring [[radioactive|radioactivities]] (α, β, and γ), only [[alpha decay]] is a type of decay resulting from the [[strong force|nuclear strong force]]. Thus, alpha-decay can be considered either a form of particle decay or, less frequently, a special case of [[nuclear fission]].  The timescale for the [[strong interaction|nuclear strong force]] is much faster than that of the [[weak interaction|nuclear weak force]] or the [[electromagnetism|electromagnetic force]], so the lifetime of nuclei past the drip lines are typically on the order of nanoseconds or less. For alpha decay, the timescale can be much longer than for proton or neutron emission owing to the high Coulomb barrier seen by an alpha-cluster in a nucleus (the alpha particle must [[quantum tunnelling|tunnel]] through the barrier).  As a consequence, there are no naturally occurring nuclei on Earth which undergo proton emission or [[neutron emission]]; however, such nuclei can be created, for example, in the laboratory with [[Particle accelerator|accelerators]] or naturally in [[Stellar nucleosynthesis|stars]].
 
Such particle decays are not commonly known because particle decay is governed by the [[Strong interaction|nuclear strong force]], as well as the Coulomb force in the case of charged particles, which can act very quickly (femtoseconds or less). In nuclear physics terms, nuclei that are outside the drip lines are particle-unbound and considered not to exist, because they can only exist in the [[Space-time continuum|energy continuum]] rather than in the discrete quantized states we are familiar with.  In a discussion of the proton and neutron drip lines, one nomenclatural convenience is to regard beta-unstable nuclei as stable (strictly speaking they are particle-stable), due to the significant difference in the time-scales of these two different decay modes.
 
Thus, the only type of nuclei which are longer lived and undergo proton or neutron emission are in the class of beta-delayed decays, where first the isospin of one nucleon is reversed (proton to neutron or vice versa) via beta-decay, and then if the particle separation energy is non-positive, the daughter nucleus will undergo particle decay.  Most naturally occurring γ-sources are technically β-delayed γ-decay, so this concept should be familiar; some gamma-sources are α-delayed but these are generally categorized with other alpha-sources.
 
==Nuclear structure origin of the drip lines==
We can see how the drip lines originate by considering the energy levels in a nucleus. The energy of a nucleon in a nucleus is its [[rest mass energy]] minus a [[binding energy]]. In addition to this, however, there is an energy due to degeneracy: for instance a nucleon with energy ''E''<sub>1</sub> will be forced to a higher energy ''E''<sub>2</sub> if all the lower energy states are filled. This is because nucleons are [[fermions]] and obey [[Fermi-Dirac statistics]]. The work done in putting this nucleon to a higher energy level results in a pressure which is the [[degeneracy pressure]].  
 
So we can view the energy of a nucleon in a nucleus as its rest mass energy minus an effective binding energy which decreases as we go to higher energy levels. Eventually this effective binding energy has become zero so that the highest occupied energy level, the [[Fermi energy]], is equal to the rest mass of a nucleon. At this point adding a nucleon of the same isospin to the nucleus is not possible, as the new nucleon would have a negative effective binding energy&nbsp;— i.e. it is more energetically favourable (system will have lowest overall energy) for the nucleon to be created outside the nucleus. This is the particle drip point for that species.
 
==Astrophysical relevance==
In [[nuclear astrophysics]] the drip lines are especially useful as limiting boundaries for [[Nucleosynthesis#Explosive_nucleosynthesis|explosive nucleosynthesis]] as well as other circumstances with extreme pressure or temperature conditions such as [[neutron star]]s.
 
===Nucleosynthesis===
Explosive astrophysical environments often have very large [[flux]]es of high energy nucleons which can be captured on [[Seed nucleus|seed nuclei]].  In these environments, radiative [[Neutron capture|captures]], whether of protons or neutrons, will be much faster than beta-decays, and as astrophysical environments with both large neutron fluxes and high energy protons are unknown at present, the reaction flow will proceed away from beta-stability towards or up to either the neutron or proton drip lines, respectively. However, once a nucleus reaches a drip line, as we have seen, no more nucleons of that species can be added to the particular nucleus, and the nucleus must first undergo a beta-decay before further nucleon captures can occur.
 
====Photodisintegration====
While the drip lines impose the ultimate boundaries for nucleosynthesis, in high energy environments the burning pathway may be limited before the drip lines by photodisintegration, where a high energy gamma ray knocks a nucleon out of a nucleus.  The same nucleus is subject both to a flux of nucleons and photons, so an equilibrium is reached where mass builds up at particular nuclear species. In this sense one might also imagine a similar drip line which applies to photodisintegration in particular environments, but because the nucleons are energetically knocked-out of nuclei and not dripping out in such a case, the terminology is misleading and is not used.
 
As the photon bath will typically be described by a [[Planck's law|Planckian distribution]], higher energy photons will be less abundant, and so photodisintegration will not become significant until the nucleon separation energy begins to approach zero towards the drip lines, where photodisintegration may be induced by lower energy gamma rays.  At 1 × 10<sup>9</sup> Kelvin, the photon distribution is energetic enough to knock nucleons out of any nuclei with particle separation energies less than 3 MeV,<ref>{{cite journal | journal=Nuclear Physics A | volume=570 | issue=1-2 | pages=329 | year=1994  | author=Thielemann, Friedrich-Karl; Kratz, Karl-Ludwig; Pfeiffer, Bernd; Rauscher, Thomas; van Wormer, Laura; Wiescher, Michael C.| title= Astrophysics and nuclei far from stability | doi =
10.1016/0375-9474(94)90299-2 | bibcode=1994NuPhA.570..329T}}</ref> but to know which nuclei exist in what abundances one must consider also the competing radiative captures.
 
As [[neutron capture]]s can proceed at any energy regime, neutron photodisintegration is unimportant except at higher energies.  However, as proton captures are inhibited by the Coulomb barrier, the cross sections for charged-particle reactions at lower energies are greatly suppressed, and in the higher energy regimes where proton captures have a large probability to occur, there is often a competition between proton capture and photodisintegration in explosive hydrogen burning; but because the proton drip line is relatively much closer to the valley of beta-stability than the neutron drip line, nucleosynthesis in some environments may proceed as far as either nucleon drip line.
 
====Waiting points and time scales====
Once radiative capture can no longer proceed on a given nucleus, either from photodisintegration or the drip lines, further nuclear processing to higher mass must either bypass this nucleus by undergoing a reaction with a heavier nucleus such as <sup>4</sup>He, or more often wait for the beta decay. Nuclear species where a significant fraction of the mass builds up during a particular nucleosynthesis episode are considered nuclear waiting points, since further processing by fast radiative captures is delayed. There is not an explicit definition of what constitutes a nuclear waiting point, and some quantitative criteria relating the mass fraction at a given nucleus for a given time with respect to the nucleosynthesis time scale is desirable.  
 
As has been emphasized, the beta-decays are the slowest processes occurring in explosive nucleosynthesis. From the nuclear physics side, explosive nucleosynthesis time scales are set simply by summing the beta decay half-lives involved,<ref>{{cite journal|journal=The Astrophysical Journal|volume=432|pages=326|year=1994|author=van Wormer, L.; Goerres, J.; Iliadis, C.; Wiescher, M.; Thielemann, F.-K.|title=Reaction rates and reaction sequences in the rp-process|doi=10.1086/174572|bibcode=1994ApJ...432..326V}}</ref> since the time scale for other nuclear processes is negligible in comparison, although practically speaking this time scale is dominated by the sum merely of a handful of waiting point nuclear half lives typically.
 
====The r-process====
The [[R-process|rapid neutron capture process]] probably operates very closely to the neutron drip line.  Thus, the reaction flow in the r-process is generally assumed to run along the neutron drip line. However, the astrophysical site of the r-process, while widely believed to take place in core-collapse supernovae, is unknown. Furthermore, the neutron drip line is very poorly determined experimentally, and nuclear mass models give various predictions for the precise location of the neutron drip line. In fact, the nuclear physics of extremely neutron-rich matter is a fairly new subject, and already has led to the discovery of the [[island of inversion]] and [[Halo nucleus|halo nuclei]] such as <sup>11</sup>Li, which in consequence of a very diffuse neutron skin, has a total radius comparable to that of <sup>208</sup>Pb. {{what?|date=December 2011}} Thus, although the neutron drip line and the r-process are linked very closely in research, it is an unknown frontier awaiting future research, both from theory and experiment.
 
====The rp-process====
The [[Rp-process|rapid proton capture process]] in [[X-ray burster|X-ray bursts]] runs at the proton drip line except near some photodisintegration waiting points.  This includes the nuclei <sup>21</sup>Mg, <sup>30</sup>S, <sup>34</sup>Ar, <sup>38</sup>Ca, <sup>56</sup>Ni, <sup>60</sup>Zn, <sup>64</sup>Ge, <sup>68</sup>Se,
<sup>72</sup>Kr, <sup>76</sup>Sr, and <sup>80</sup>Zr.<ref>{{cite journal | journal=Astronomy and Astrophysics | volume=342 | pages=464 | year=1999  | author=Koike, O.; Hashimoto, M.; Arai, K.; Wanajo, S.| title= Rapid proton capture on accreting neutron stars&nbsp;– effects of uncertainty in the nuclear process | bibcode=1999A&A...342..464K}}</ref><ref name="Fisker2008">{{cite journal | journal=The Astrophysical Journal Supplement Series | volume=174 | issue=1 | pages=261 | year=2008  | author=Fisker, Jacob Lund; Schatz, Hendrik; Thielemann, Friedrich-Karl| title= Explosive Hydrogen Burning during Type I X-Ray Bursts | doi = 10.1086/521104 | bibcode=2008ApJS..174..261F}}</ref> 
 
One obvious nuclear structure pattern that emerges is the importance of [[Nuclear_structure#Nuclear_pairing_phenomenon|pairing]], as one notices all the waiting points above are at nuclei with an even number of protons, and all but <sup>21</sup>Mg also have an even number of neutrons.  However, the waiting points will depend on the assumptions of the X-ray burst model, such as [[metallicity]], accretion rate, and the hydrodynamics, along with of course the nuclear uncertainties, and as mentioned above, the exact definition of the waiting point may not be consistent from one study to the next. Although there are nuclear uncertainties, compared to other explosive nucleosynthesis processes, the rp-process is quite well experimentally constrained, as, for example, all the above waiting point nuclei have at the least been observed in the laboratory. Thus as the nuclear physics inputs can be found in the literature or data compilations, the [http://www.nucastrodata.org/infrastructure.html  Computational Infrastructure for Nuclear Astrophysics] allows one to do post-processing calculations on various X-ray burst models, and define for oneself the criteria for the waiting point, as well as alter any nuclear parameters.
 
While the rp-process in X-ray bursts may have difficulty by-passing the <sup>64</sup>Ge waiting point,<ref name="Fisker2008" /> certainly in [[X-ray pulsars]] where the rp-process is stable, the alpha drip line places an upper limit near A=100 on the mass which can be reached through continuous burning;<ref>{{cite journal | last = Schatz | first = H. | coauthors = A. Aprahamian, V. Barnard, L. Bildsten, A. Cumming, M. Ouellette, T. Rauscher, F.-K. Thielemann, and M. Wiescher |date=April 2001 | title = End Point of the ''rp'' Process on Accreting Neutron Stars | journal = Physical Review Letters | pmid = 11328001 | volume = 86 | issue = 16 | pages = 3471–3474 | doi = 10.1103/PhysRevLett.86.3471 | url = http://link.aps.org/abstract/PRL/v86/p3471 | accessdate = 2006-08-24 | format = subscription required | bibcode=2001PhRvL..86.3471S|arxiv = astro-ph/0102418 }}</ref> the exact location of the alpha drip line is a present matter under investigation, and <sup>106</sup>Te is known to alpha-decay whereas <sup>103</sup>Sb is particle-bound.  However, it has been shown that if there are episodes of cooling or mixing of previous ashes into the burning zone, material as heavy as <sup>126</sup>Xe can be created.<ref>{{cite journal | author = Koike, Osamu; Hashimoto, Masa-aki; Kuromizu, Reiko; Fujimoto, Shin-ichirou| year = 2004 | title = Final Products of the rp-Process on Accreting Neutron Stars | journal = The Astrophysical Journal | volume = 603 | issue = 1 | pages = 242–251 | doi = 10.1086/381354 | bibcode = 2004ApJ...603..242K | format = subscription required}}</ref>
 
===Neutron stars===
In neutron stars, neutron heavy nuclei are found as relativistic electrons penetrate the nuclei and produce [[inverse beta decay]], wherein the electron combines with a proton in the nucleus to make a neutron and an electron-neutrino:
 
<!-- Autogenerated using Phykiformulae 0.12 [[User:SkyLined#Phykiformulae]]
p + e -> n + ve
-->:{| border="0"
|- style="height:2em;"
|{{Subatomic particle|link=yes|Proton}}&nbsp;||+&nbsp;||{{Subatomic particle|link=yes|Electron}}&nbsp;||→&nbsp;||{{Subatomic particle|link=yes|Neutron}}&nbsp;||+&nbsp;||{{Subatomic particle|link=yes|Electron Neutrino}}
|}
 
As more and more neutrons are created in nuclei the energy levels for neutrons get filled up to an energy level equal to the rest mass of a neutron. At this point any electron penetrating a nucleus will create a neutron which will "drip" out of the nucleus. At this point we have:
 
: <math> E_F^n=m_n c^2 \,</math>
 
And from this point onwards the equation
 
: <math> E_F^n=\sqrt{(p_F^n)^2c^2 + m_n^2 c^4} \,</math>
 
applies, where ''p''<sub>''F''</sub><sup>''n''</sup> is the [[Fermi momentum]] of the neutron. As we go deeper into the neutron star the free neutron density increases, and as the Fermi momentum increases with increasing density, the [[Fermi energy]] increases, so that energy levels lower than the top level reach neutron drip and more and more neutrons drip out of nuclei so that we get nuclei in a neutron fluid. Eventually all the neutrons drip out of nuclei and we have reached the neutron fluid interior of the neutron star.
 
==Known values==
===Neutron drip line===
The values of the neutron drip line are only known for the first eight elements, hydrogen to oxygen.<ref>{{cite web|url=http://www.sciencedaily.com/releases/2007/10/071024130508.htm |title=Three First-ever Atomic Nuclei Created; New Super-heavy Aluminum Isotopes May Exist |publisher=Sciencedaily.com |date=2007-10-27 |accessdate=2010-04-06}}</ref> For ''Z''&nbsp;=&nbsp;8, the maximal number of neutrons is 16, resulting in O-24 as the heaviest possible oxygen isotope.<ref>{{cite web|url=http://www.sciencedaily.com/releases/2007/09/070913170108.htm |title=Nuclear Physicists Examine Oxygen's Limits |publisher=Sciencedaily.com |date=2007-09-18 |accessdate=2010-04-06}}</ref>
 
===Proton drip line===
The general location of the proton drip line is well established.  For all elements occurring naturally on earth and having an odd number of protons, at least one species with a proton separation energy less than zero has been experimentally observed.  Up to [[germanium]] the location of the drip line for many elements with an even number of protons is known, but none past that point are listed in the evaluated nuclear data.  There are a few exceptional cases where, due to [[Nuclear structure#Nuclear pairing phenomenon|nuclear pairing]], there are some particle-bound species outside the drip line, such as [[Isotopes of boron|<sup>8</sup>B]] and [[Isotopes of gold|<sup>178</sup>Au]].  One may also note that nearing the [[Magic number (physics)|magic numbers]], the drip line is less understood.  A compilation of the known first unbound nuclei beyond the proton drip line is given below, with the [[Atomic number|number of protons, Z]] and the corresponding isotopes, taken from the National Nuclear Data Center.<ref>{{cite web| title = National Nuclear Data Center|  url = http://www.nndc.bnl.gov| accessdate = 2010-04-13}}</ref>
 
{| border="1"
! Z !! Species
|-
| 1 || N/A
|-
| 2 || <sup>2</sup>He
|-
| 3 || <sup>5</sup>Li
|-
| 4 || <sup>5</sup>Be
|-
| 5 || <sup>7</sup>B, <sup>9</sup>B
|-
| 7 || <sup>11</sup>N
|-
| 8 || <sup>12</sup>O
|-
| 9 || <sup>16</sup>F
|-
| 11|| <sup>19</sup>Na
|-
| 12|| <sup>19</sup>Mg
|-
| 13|| <sup>21</sup>Al
|-
| 15|| <sup>25</sup>P
|-
| 17|| <sup>30</sup>Cl
|-
| 19|| <sup>34</sup>K
|-
| 21|| <sup>39</sup>Sc
|-
| 23|| <sup>42</sup>V
|-
| 25|| <sup>45</sup>Mn
|-
| 27|| <sup>50</sup>Co
|-
| 29|| <sup>55</sup>Cu
|-
| 31|| <sup>59</sup>Ga
|-
| 32|| <sup>58</sup>Ge
|-
| 33|| <sup>65</sup>As
|-
| 35|| <sup>69</sup>Br
|-
| 37|| <sup>73</sup>Rb
|-
| 39|| <sup>77</sup>Y
|-
| 41|| <sup>81</sup>Nb
|-
| 43|| <sup>85</sup>Tc
|-
| 45|| <sup>89</sup>Rh
|-
| 47|| <sup>93</sup>Ag
|-
| 49|| <sup>97</sup>In
|-
| 51|| <sup>105</sup>Sb
|-
| 53|| <sup>110</sup>I
|-
| 55|| <sup>115</sup>Cs
|-
| 57|| <sup>119</sup>La
|-
| 59|| <sup>123</sup>Pr
|-
| 61|| <sup>128</sup>Pm
|-
| 63|| <sup>134</sup>Eu
|-
| 65|| <sup>139</sup>Tb
|-
| 67|| <sup>145</sup>Ho
|-
| 69|| <sup>149</sup>Tm
|-
| 71|| <sup>155</sup>Lu
|-
| 73|| <sup>159</sup>Ta
|-
| 75|| <sup>165</sup>Re
|-
| 77|| <sup>171</sup>Ir
|-
| 79|| <sup>175</sup>Au, <sup>177</sup>Au
|-
| 81|| <sup>181</sup>Tl
|-
| 83|| <sup>189</sup>Bi
|-
| 85|| <sup>195</sup>At
|-
| 87|| <sup>201</sup>Fr
|-
| 89|| <sup>207</sup>Ac
|-
| 91|| <sup>214</sup>Pa
|}
 
==See also==
* [[Extension of the periodic table beyond the seventh period]]
* [[Period 8 element]]
* [[Table of nuclides]]
* [[Radioactive decay]]
 
==References==
{{Reflist|2}}
 
[[Category:Nuclear physics]]
[[Category:Nucleosynthesis]]

Latest revision as of 11:55, 31 August 2014

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