A number of people have asked about appropriate prayers for Yom Ha'atzmaut. Here are some brief notes.
It is very important to have hakarat hatov (gratitude) to G-d and to recognise the importance of Yom Ha'atzmaut, a day which marks the declaration of the State of Israel.
How can we express this?
If you can, try to have a seuda, festive meal. This does not need to be a visit to a restaurant! Buy and ice cream or a smoked salmon sandwich, for example, if that makes your lunch a bit more special! Food helps us to develop an internal appreciation of a special event.
Psalm 126 (the 'Shir hama'alot) before Birkat Hamazon (benching) was one of the candidates to be the Israeli national anthem. It is a very appropriate Psalm. Psalm 107 is in the same vein. The prayer for the State of Israel is also appropriate.
Hallel is also appropriate for Yom Ha'atzmaut. The green siddur notes that some communities recite Hallel with a beracha (blessing) whilst others do not. What is the reason for this non-prescriptive note?
Reciting Hallel and reciting a beracha are in fact two separate questions, none of which have anything to do in this context with negativity towards Zionism. They also give a glimpse into the methodology of Jewish law, which lawyers may particularly appreciate!
Saying a beracha
Based on the second of the 10 commandments, 'lo tisa' (do not take G-d's Name in vain), some Poskim (Halachic authorities / authorities in Jewish law) rule that if there is a doubt as to whether a beracha should be said in a particular situation, then the beracha should not be recited due to lo tisa.
To use a familiar example from this time of the year, if you are about to go to sleep are not sure whether you counted the Omer that night or not, you should count without saying the beracha. Why? If you already have counted, then saying the beracha again could be taking G-d's Name in vein as the counting is the actual mitzva and the beracha is just an introduction to focus you, so therefore you can perform the mitzva without saying the beracha.
Why might there be a doubt as to whether to say a Beracha for Hallel on Yom Ha'atzmaut?
The Talmud (Pesachim 117a) discusses when there is an obligaition to say Hallel. Various conditions must be fulfiled for Hallel to be said. For example, these conditions include whether a particular salvation took place on a particular day, how many people were saved, what the outcome of the salvation was.
It is noteworthy, for example, that we do not say Hallel on Purim. Amongst other reasons, the outcome of the salvation in the Purim story was that we were almost back to square 1, so to speak, since despite the salvation we were still servants of King Achashvairosh.
Applying the Halachic conditions of when to say Hallel to the facts of Yom Ha'atzmaut in 1948, it is hard to arrive at a definitive conclusion as to whether Yom Ha'atzmaut requires the recitation of Hallel or other prayers which may be more appropriate.
Some Poskim hold that Hallel should be recited with a beracha since they feel that all of the conditions are satisfied.
Others hold a 'middle position' that since we are not sure if Hallel should be recited, we can say it without a beracha (this is the position of the Chief Rabbinate of Israel). How does this work? The contents of Hallel are very appropriate Psalms which we can certainly say for Yom Ha'atzmaut and help us to acknowledge that it is a special day. Since we can say these Psalms without the beracha of Hallel (either at the start of the finish of Hallel), the beracha is not essential as in the example of the Omer above. By not saying the beracha, we avoid infringing lo tisa in case Yom Ha'atzmaut does not tick all of the boxes required for definately saying Hallel.
Conclusion
Regarding Hallel, each community should follow its own position based on a reputable Posek (singular of Poskim), as reflected in the non-prescriptive instuctions in the green Siddur. In South Hampstead, we follow the position of the Chief Rabbinate of Israel.
If you cannot say Hallel, try to eat something special for the day to try and develop an internal appreciation that this is a special day and say one of the Psalms linked above.
If you want to sing or listen to Hatikva (Israel's national anthem), look at this which is a stirring rendition. Hebrew words and translation are at the bottom of here. Transliteration is at point 3 here. Look here for a broadcast from 1948 in Hebrew including a short clip of David Ben-Gurion reading the declaration of independence.
For a great and detailed Yom Ha'atzmaut resource, go to Yeshiva University's resource pack here .
Chag Ha'atzmaut Sameach!